A Talenti Comparison Result for Solutions to Elliptic Problems with Robin Boundary Conditions
Angelo Alvino, Carlo Nitsch, Cristina Trombetti
Abstract
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.
Topics & Concepts
MathematicsRobin boundary conditionBoundary (topology)Dirichlet distributionDirichlet boundary conditionBoundary value problemDimension (graph theory)PlanarMixed boundary conditionMathematical analysisApplied mathematicsPure mathematicsComputer scienceComputer graphics (images)Nonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringSpectral Theory in Mathematical Physics