A talenti comparison result for solutions to elliptic problems with Robin boundary conditions. (English) Zbl 1525.35076
Summary: 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. published by Wiley Periodicals LLC.}
{© 2023 The Authors. published by Wiley Periodicals LLC.}
MSC:
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35J25 | Boundary value problems for second-order elliptic equations |
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