A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions

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...

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Veröffentlicht in:Communications on pure and applied mathematics 2023-03, Vol.76 (3), p.585-603
Hauptverfasser: Alvino, Angelo, Nitsch, Carlo, Trombetti, Cristina
Format: Artikel
Sprache:eng
Schlagworte:
Applications of mathematics
Boundary conditions
Dirichlet problem
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Zusammenfassung: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.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.22090