We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex‐valued potentials in dimensions one, two and three.

We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed unit ball of the bidual in the infinite dimensional case). We show that this set is strongly c ‐algebrable for all separable Banach spaces. For specific spaces including

In this note we are concerned with interior regularity properties of the p‐Poisson problem Δ p ( u ) = f with p > 2 . For all 0 < λ ≤ 1 we constuct right‐hand sides f of differentiability − 1 + λ such that the (Besov‐) smoothness of corresponding solutions u is essentially limited to 1 + λ / ( p − 1 ) . The statements are of local nature and cover all integrability parameters. They particularly imply

This paper first defines operators that are “well‐localized” with respect to a pair of accretive functions and establishes a global two‐weight T b theorem for such operators. Then it defines operators that are “well‐localized” with respect to a pair of accretive systems and establishes a local two‐weight T b theorem for them. The proofs combine recent T b proof techniques with arguments used to prove

In this paper, we study the following chemotaxis system with singular sensitivity and logistic source u t = Δ u − χ ∇ · u v ∇ v + r u − μ u k , x ∈ Ω , t > 0 , v t = Δ v − v + u , x ∈ Ω , t > 0 , in a smooth bounded convex domain Ω ⊂ R n ( n ≥ 2 ) with the non‐flux boundary, where χ , r , μ > 0 , k > 2 . The boundedness of solutions has been proved in the case that n ≥ 2 , k > 3 ( n + 2 ) n + 4 and

In this paper, we establish the L p ‐norm ( 1 < p ≤ ∞ ) algebraic decay rate of solutions and higher‐order derivative of solutions for 3D generalized Hall‐MHD system provided that the L1‐norm of initial data is sufficiently small and the parameters α ∈ 5 4 , 2 , β ∈ 7 4 , 2 .

We prove the existence of at least three weak solutions to a mixed Dirichlet–Neumann boundary value problem for equations driven by the p ( z ) ‐Laplace operator in the principal part. Our approach is variational and use three critical points theorems.

Our aim in this paper is to establish Hardy–Sobolev inequality for Sobolev functions in central Herz–Morrey spaces. As an application, we are concerned with Sobolev‐type integral representation for a C1‐function on R N which vanishes on the unit ball.

In this paper, we consider the following weakly coupled nonlinear Schrödinger system − ε 2 Δ u 1 + V 1 ( x ) u 1 = | u 1 | 2 p − 2 u 1 + β | u 1 | p − 2 | u 2 | p u 1 , x ∈ R N , − ε 2 Δ u 2 + V 2 ( x ) u 2 = | u 2 | 2 p − 2 u 2 + β | u 2 | p − 2 | u 1 | p u 2 , x ∈ R N , where ε > 0 , β ∈ R is a coupling constant, 2 p ∈ ( 2 , 2 ∗ ) with 2 ∗ = 2 N N − 2 if N ≥ 3 and + ∞ if N = 1 , 2 , V1 and V2 belong

In this article we prove upper bounds for the Laplace eigenvalues λ k below the essential spectrum for strictly negatively curved Cartan–Hadamard manifolds. Our bound is given in terms of k2 and specific geometric data of the manifold. This applies also to the particular case of non‐compact manifolds whose sectional curvature tends to − ∞ , where no essential spectrum is present due to a theorem of

Let T : Y → X be a bounded linear operator between two real normed spaces. We characterize compactness of T in terms of differentiability of the Lipschitz functions defined on X with values in another normed space Z. Furthermore, using a similar technique we can also characterize finite rank operators in terms of differentiability of a wider class of functions but still with Lipschitz flavour. As an

The Douady space of compact subvarieties of a Kähler manifold is equipped with the Weil–Petersson current, which is everywhere positive with local continuous potentials, and of class C ∞ when restricted to the locus of smooth fibers. There a Quillen metric is known to exist, whose Chern form is equal to the Weil–Petersson form. In the algebraic case, we show that the Quillen metric can be extended

We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the ground state for the equation with radially symmetric initial data. We then establish blow‐up criteria for non‐radial solutions to the equation. In the defocusing case

In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a + b ∫ R 3 ( − Δ ) s 2 u 2 d x ( − Δ ) s u + V ( x ) u = Q ( x ) f ( u ) + | u | 2 s ∗ − 2 u , x ∈ R 3 , where a , b > 0 , ( − Δ ) s is the fractional Laplace operator with s ∈ ( 3 4 , 1 ) , V vanishes at infinity and 2 s ∗ = 6 3 − 2 s . Under appropriate assumptions on f, we prove the existence of positive

Meromorphic solutions of non‐linear differential equations of the form f n + P ( z , f ) = h are investigated, where n ≥ 2 is an integer, h is a meromorphic function, and P ( z , f ) is differential polynomial in f and its derivatives with small functions as its coefficients. In the existing literature this equation has been studied in the case when h has the particular form h ( z ) = p 1 ( z ) e α

In this article we make a classification of four‐dimensional gradient almost Ricci solitons with harmonic Weyl curvature. We prove first that any four‐dimensional (not necessarily complete) gradient almost Ricci soliton ( M , g , f , λ ) with harmonic Weyl curvature has less than four distinct Ricci‐eigenvalues at each point. If it has three distinct Ricci‐eigenvalues at each point, then ( M , g )

We give a possible extension of definition of shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We define the divergence operator and determine the vector fields with divergence. Given the non‐existence of quaternionic volume form on H2, we define automorphisms with volume to be time‐one maps of vector fields with

In this paper we consider a LES model for the approximation of large scales of the 3D Boussinesq equations. We analyze the convergence rate, in appropriate norms, of the unique regular weak solution of the regularized Boussinesq equations towards a weak solution of the original Boussinesq system.

We consider the Riemann problem for a two‐dimensional steady pressureless relativistic Euler equations. The delta shock wave is discovered in the Riemann solutions. It is shown that Dirac delta function develops in the state variable describing the number density of particles. By virtue of a suitable generalized Rankine–Hugoniot relation and entropy condition, we establish the existence and uniqueness

Let ( X , d , μ ) be a space of homogeneous type, with upper dimension μ, in the sense of R. R. Coifman and G. Weiss. Let η be the Hölder regularity index of wavelets constructed by P. Auscher and T. Hytönen. In this article, the authors introduce the local Hardy space h ∗ , p ( X ) via local grand maximal functions and also characterize h ∗ , p ( X ) via local radial maximal functions, local non‐tangential

Topological measures and quasi‐linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set function on open and closed sets which is finitely additive on compact sets, inner regular on open sets, and outer regular on closed sets. Deficient topological

In this paper, motivated by a question posed by H. de Alba and D. T. Hoang, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorithm to find an induced matching for such graphs and we prove that this algorithm indeed gives a maximum induced matching. Applying this algorithm, we provide a strongly biconvex graph whose (monomial) edge

We consider an infinite strip Ω L = ( 0 , 2 π L ) d − 1 × R , d ≥ 2 , L > 0 , and study the control problem of the heat equation on Ω L with Dirichlet or Neumann boundary conditions, and control set ω ⊂ Ω L . We provide a sufficient and necessary condition for null‐controllability in any positive time T > 0 , which is a geometric condition on the control set ω. This is referred to as “thickness with

We consider perturbed quadharmonic operators, Δ 4 + V , acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential V satisfying a bound from below by a non‐positive function depending on the distance from a point. Under a bounded geometry assumption on the Hermitian vector bundle and the underlying Riemannian manifold, we give a sufficient condition for

We study some new summability properties of multilinear operators. We introduce the concepts of φ‐summing, φ semi‐integral and φ‐dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for φ‐summing operators, providing also a characterization of φ‐dominated operators in terms of factorizations. We analyze vector‐valued inequalities associated to

The main focus of this paper is to present a method to construct new stable equivalences of Morita type. Suppose that a B‐A‐bimodule N define a stable equivalence of Morita type between finite dimensional algebras A and B. Then, for any generator X of the A‐module category and any finite admissible set Φ of natural numbers, the Φ‐Beilinson–Green algebras G A Φ ( X ) and G B Φ ( N ⊗ A X ) are stably

We present an explicit Milnor open book decomposition supporting the canonical contact structure on the link of each minimally elliptic singularity whose fundamental cycle Z satisfies − 3 ≤ Z · Z ≤ − 1 . For the Milnor open books whose pages have genus less than three, we give a factorization of the monodromy which does not involve any left‐handed Dehn twists around interior curves. Necessary results

We provide a study of Köthe sequence algebras. These are Fréchet sequence algebras which can be viewed as abstract analogoues of algebras of smooth or holomorphic functions. Of particular treatment are the following properties: unitality, m‐convexity, Q‐property and variants of amenability. These properties are then checked against the topological ( DN ) ‐(Ω) type conditions of Vogt–Zaharjuta. Description

Let S n be a symmetric simple random walk on the integer lattice Z d . For a Bernstein function ϕ we consider a random walk S n ϕ which is subordinated to S n . Under a certain assumption on the behaviour of ϕ at zero we establish global estimates for the transition probabilities of the random walk S n ϕ . The main tools that we apply are a parabolic Harnack inequality and appropriate bounds for the

In this paper we consider laminated beams modelled from the well established Timoshenko system, which is a structure given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. By using semi‐group approach, we prove the global well‐posedness of the system when a viscoelastic dissipation

In this work we propose a Filippov‐type lemma for the differential inclusion d d μ x ( t ) ∈ F ( t , x ( t ) ) , x ( 0 ) = x 0 , (0.1)where F : [ 0 , T ] × R d ⇝ R d is a given multifunction and μ is a finite Borel signed measure on [0, T] (possibly atomic). By a solution of (0.1) we mean a function x : [ 0 , T ] ⟶ R d such that x ( 0 ) = x 0 and x ( t ) = x 0 + ∫ S ( t ) v ( s ) d μ ( s ) for t >

We study a class of nonlinear elliptic equations involving measure data − div A ( x , D u ) = μ in Ω , where μ is a Radon measure. Under the main assumption of A ( x , ξ ) that there exists a constant Λ > 0 such that | A ( x , ξ ) − A ( x 0 , ξ ) | ≤ Λ ( a ( x ) + a ( x 0 ) ) | x − x 0 | α ( | ξ | 2 + s 2 ) p − 1 2 , α ∈ ( 0 , 1 ] , where 0 ≤ a ( x ) ∈ L m ( Ω ) for some integrable index m > 1 , we

In this paper, we discuss a diffusive predator‐prey model with predator cannibalism in spatially heterogeneous environments. In contrast with spatially homogeneous environments, we find the dynamics of the model in spatially heterogenous environments is more complicated. For the spatially heterogeneous case, we could classify death rate of the predator into four different regions and demonstrate that

We consider two versions of the uniform Roe algebra for uniformly discrete spaces without bounded geometry and discuss some of their properties.

We prove a weighted Sobolev trace embedding in the upper half‐space and give its best constant. This embedding can be employed to study a number of critical boundary problems. In this direction, we obtain existence and nonexistence results for a class of semilinear elliptic equations with nonlinear boundary conditions involving critical growth. These equations are closely related to the study of self‐similar

In this work, we prove the local well‐posedness of local strong solutions to an isentropic compressible Ginzburg–Landau–Navier–Stokes system with vacuum in a bounded domain Ω ⊂ R 3 .

We study some classical uniqueness and existence results, such as Peano's or Osgood's uniqueness criteria, in the context of Stieltjes differential equations. This type of equation is based on derivatives with respect to monotone functions, and enables the investigation of discrete and continuous problems from a common standpoint. We compare our results with previous work on the topic and illustrate

The main focus of this paper is on study of s‐numbers for a higher order Sobolev embedding on an interval and also for the corresponding Hardy‐type operator. Upper and lower estimates for approximation and Bernstein numbers are described and their relations with results for lower order Sobolev embeddings are discussed.

In this paper, we investigate the Hausdorff dimension of the invariant measures of the iterated function system (IFS) { α x , β x , γ x + ( 1 − γ ) } . We provide an “almost every” type result by a direct application of the results of Feng and Hu [5] and Kamalutdinov and Tetenov [9].

We prove L p estimates, 1 ≤ p ≤ ∞ , for solutions to the tangential Cauchy–Riemann equations ∂ ¯ b u = ϕ on a class of infinite type domains Ω ⊂ C 2 . The domains under consideration are a class of convex ellipsoids, and we show that if ϕ is a ∂ ¯ b ‐closed (0,1)‐form with coefficients in L p , then there exists an explicit solution u satisfying ∥ u ∥ L p ( b Ω ) ≤ C ∥ ϕ ∥ L p ( b Ω ) . Moreover, when

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution { u , p } of the Navier–Stokes equation such that | ∇ j u ( t , x ) | = O ( | x | 1 − n − j ) and | ∇ j p ( t , x ) | = O ( | x |

In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces.

We give a classification of real hypersurfaces in the complex hyperbolic quadric Q m ∗ = S O 2 , m o / S O 2 S O m that have constant mean curvature and harmonic curvature.

We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the form x f ( x ) , where f is itself the Laplace transform of a sum of dilations and translations of periodic functions. Our methods are also applied to ratios

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.

Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE ‐singularities. Let G be the reductive group given by the root system of these singularities. We construct a G‐torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical

In this paper, we define and study Gevrey spaces associated with a Hörmander family of (globally defined) vector fields and its corresponding sub‐Laplacian. We show some natural relations between the various Gevrey spaces in this setting on general manifolds, and more particular properties on Lie groups with polynomial growth of the volume. In the case of the Heisenberg group and of S U ( 2 ) , we

It is a classical result that every C ‐valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E over C . Motivated by this example we try to answer the following question. Let E be a locally convex Hausdorff space over a field K , let F ( Ω ) be a locally convex Hausdorff

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups in the characteristic case via the Fichera function. Probabilistically, our result may be stated as follows: We construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves continuously in the interior of the state space, without reaching the boundary

We consider 3‐dimensional pseudo‐manifolds M ̂ with a given set of marked point V such that M ̂ ∖ V is the interior of a compact 3‐manifold with boundary M. An ideal triangulation T of ( M ̂ , V ) has V as set of vertices. A branching ( T , b ) enhances T to a Δ‐complex. Branched triangulations of ( M ̂ , V ) are considered up to the b‐transit equivalence generated by isotopy and ideal branched moves

For a character χ of a finite group G, the number χ c ( 1 ) = [ G : ker χ ] χ ( 1 ) is called the codegree of χ. Let N be a normal subgroup of G and set Irr ( G | N ) = Irr ( G ) − Irr ( G / N ) . Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of | N | , p q divides none of the codegrees of elements of Irr ( G | N ) , then Fit ( N ) ≠ { 1 } and N is either

The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space H Φ ( R n ) to another Orlicz–Hardy space H Ψ ( R n ) , where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator I α from H p ( R n ) to H q ( R n ) for α , p , q ∈ ( 0 , ∞ ) and − n / p + α = − n / q , which was proved by Stein and Weiss

We prove the existence and uniqueness of μ‐pseudo almost automorphic solution for a delayed non‐autonomous partial functional differential equation in the exponential dichotomic case, where the nonlinear operator F satisfies the φ‐Lipschitz condition and φ belongs to some admissible spaces. We further prove the existence of an invariant stable manifold around the μ‐pseudo almost automorphic solution

This paper is concerned with the following elliptic problem: ( − Δ ) m u = u + m ∗ − 1 + λ u − s 1 φ 1 , in B 1 , u ∈ D 0 m , 2 ( B 1 ) , ( P ) (P)where ( − Δ ) m is the polyharmonic operator, m ∗ = 2 N N − 2 m is the critical Sobolev embedding exponent. B1 is the unit ball in R N , s1 and λ > 0 are parameters, φ 1 > 0 is the eigenfunction of ( − Δ ) m , D 0 m , 2 ( B 1 ) corresponding to the first

For q ≥ 1 we consider the nonlocal ordinary differential equation − a ∫ 0 1 | y | q d s y ′ ′ ( t ) = λ f ( t , y ( t ) ) , 0 < t < 1 , subject to the Dirichlet boundary conditions y ( 0 ) = 0 = y ( 1 ) . Due to the term a ∫ 0 1 | y | q ds appearing in the equation, this is a class of nonlocal differential equations. By using a novel order cone we are able to establish existence of a positive solution

This paper is concerned with well‐posedness of the Cahn–Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu–Wu (Arch. Ration. Mech. Anal. 233 (2019), 167–247) via an energetic variational approach and it naturally fulfils three physical constraints such as mass conservation, energy dissipation and force balance. The target problem examined

We consider weak solutions ( u , π ) : Ω → R n × R to stationary p‐Stokes systems of the type − div a ( x , E u ) + ∇ π + [ D u ] u = f , div u = 0 in Ω ⊂ R n , where the function a ( x , ξ ) satisfies p‐growth conditions in ξ and depends Hölder continuously on x. By E u we denote the symmetric part of the gradient D u and we write [ D u ] u for the convective term. In this setting, we establish results

We prove an extension theorem for ultraholomorphic classes defined by so‐called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, more precisely we are working with real methods by applying the ultradifferentiable

Following Mumford and Chiodo, we compute the Chern character of the derived pushforward ch ( R • π * O ( D ) ) , for D an arbitrary element of the Picard group of the universal curve over the moduli stack of stable marked curves. This allows us to express the pullback of universal Brill–Noether classes via Abel–Jacobi sections to the compactified universal Jacobians, for all compactifications such