In this paper we build up a criteria for fractional Orlicz–Sobolev extension and imbedding domains on Ahlfors $n$-regular domains.

Let $X = [0, 1]^n, n \geq 1$. We show that the typical (in the sense of Baire category) compact subset of $X$ is not only a zero dimensional Cantor space but it satisfies the property of being strongly microscopic, which is stronger than dimension zero.

We deal with the following nonlinear problem involving fractional $p\&q$ Laplacians: \begin{equation*} (-\Delta)^{s}_{p}u+(-\Delta)^{s}_{q}u+|u|^{p-2}u+|u|^{q-2}u=\lambda h(x) f(u)+|u|^{q^{*}_{s}-2}u \quad \mbox{in } \mathbb{R}^{N}, \end{equation*} where $s\in (0,1)$, $1 < p < q < \frac{N}{s}$, $\q=\frac{Nq}{N-sq}$, $\lambda > 0$ is a parameter, $h$ is a nontrivial bounded perturbation and $f$ is a

We present a partial Hölder regularity result for the gradient of solutions to quasimonotone systems: $$\mathrm div \:\mathbf A(\cdot,D\mathbf u) = \mathbf B(\cdot, D\mathbf u) \quad \text{in } \Omega,$$ on bounded domains in the weak sense. Here certain continuity, uniformly strictly quasimonotonicity, growth conditions are imposed on the coefficients, including an asymptotic Uhlenbeck behaviour close

A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful tool that is the workhorse of many methods both in mathematics and applied fields. A prominent application in recent years is the approximation of high-dimensional functions in a low-rank format. This is based on the fact