A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions |
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| Authors: | Angelo Alvino Carlo Nitsch Cristina Trombetti |
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| Affiliation: | 1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università degli Studi di Napoli “Federico II” Complesso Universitario Monte S. Angelo, via Cintia, 80126 Napoli, Italy;2. Dipartimento di Matematica e Applicazioni Università degli Studi di Napoli “Federico II” Complesso Universitario Monte S. Angelo, via Cintia, 80126 Napoli, Italy |
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| Abstract: | Comparison results of Talenti type for elliptic problems with Dirichlet boundary conditions have been widely investigated in recent decades. In this paper, we deal with Robin boundary conditions. Surprisingly, contrary to the Dirichlet case, Robin boundary conditions make the comparison sensitive to the dimension, and while the planar case seems to be completely settled, in higher dimensions some open problems are yet unsolved. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. |
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