• 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
• 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
• 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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