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arXiv · 2504.06103

Talenti comparison results for solutions to $p$-Laplace equation on multiply connected domains

Luca Barbato·Francesco Salerno
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Abstract

In the last years comparison results of Talenti type for Elliptic Problems have been widely investigated. In this paper we obtain a comparison result for the $p$-Laplace operator in multiply connected domains with Robin boundary condition on the exterior boundary and non-homogeneous Dirichlet boundary conditions on the interior one, generalizing the results obtained in \cite{ANT, AGM} to this type of domains. This will be a generalization to Robin boundary condition of the results obtained in \cite{B, B2}, with an improvement of the $L^2$ comparison in the case $p=2$. As a consequence, we obtain a Bossel-Daners and Saint-Venant type inequalities for multiply connected domains.

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Luca Barbato, Francesco Salerno. 2025-04-08. Talenti comparison results for solutions to $p$-Laplace equation on multiply connected domains. https://arxiv.org/abs/2504.06103

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