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

2025/04/08 by Barbato, Luca, Salerno, Francesco · 3 citations
#35B51 #35J92 #35P30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.06103

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 \citeANT, AGM to this type of domains. This will be a generalization to Robin boundary condition of the results obtained in \citeB, B2, with an improvement of the L² 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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• On the stability of the annulus for the torsion of multiply connected domains
• Estimates for the first and second Steklov-Dirichlet eigenvalues
• Optimality and stability of the radial shapes for the Sobolev trace constant

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