Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions

Alba Lia Masiello () and Gloria Paoli ()
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Alba Lia Masiello: Università degli studi di Napoli Federico II, Via Cintia, Complesso Universitario Monte S. Angelo
Gloria Paoli: Università degli studi di Napoli Federico II, Via Cintia, Complesso Universitario Monte S. Angelo

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 2, No 5, 628-648

Abstract: Abstract Let $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n be an open, bounded and Lipschitz set. We consider the Poisson problem for the p-Laplace operator associated to $$\Omega $$ Ω with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison: we prove that the equality is achieved only if $$\Omega $$ Ω is a ball and both the solution u and the right-hand side f of the Poisson equation are radial and decreasing.

Keywords: Robin boundary conditions; p-Laplace operator; Rigidity result; Talenti comparison; 35J92; 35J25; 46E30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02442-1

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