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  • Sharp regularity for the inhomogeneous porous medium equation
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-25
    Damião J. Araújo, Anderson F. Maia, José Miguel Urbano

    We show that locally bounded solutions of the inhomogeneous porous medium equation $$u_{t}-\operatorname{div}\left(m|u|^{m-1} \nabla u\right)=f \in L^{q, r}, \quad m>1$$ are locally Hölder continuous, with exponent $$\gamma = \min \{ {{\alpha _0^ - } \over m},\;{{[(2q - n)r - 2q]} \over {q[(mr - (m - 1)]}}\} ,$$ where α0 denotes the optimal Hölder exponent for solutions of the homogeneous case. The

    更新日期:2020-03-25
  • Cesàro bounded operators in Banach spaces
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-25
    Teresa Bermúdez, Antonio Bonilla, Vladimír Müller, Alfredo Peris

    We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Cesàro bounded and strongly Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing (hence, not power bounded) absolutely Cesàro bounded operators on ℓp(ℕ), 1 ≤ p < ∞, and provide examples of uniformly

    更新日期:2020-03-25
  • A Schwarz lemma at the boundary on complex Hilbert balls and applications to starlike mappings
    J. Anal. Math. (IF 0.949) Pub Date : 2020-03-23
    Ian Graham, Hidetaka Hamada, Gabriela Kohr

    In this paper, we prove a Schwarz lemma at the boundary for holomorphic mappings f between Hilbert balls, and obtain related consequences. Especially, we obtain estimations of ∥Df(z0)∥ on the holomorphic tangent space for holomorphic mappings f or for homogeneous polynomial mappings f between Hilbert balls. Next, we prove the boundary rigidity theorem for holomorphic self-mappings of a Hilbert ball

    更新日期:2020-03-23
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