A domain perturbation problem for the Poisson equation

Abstract

We consider an approach based on the Functional Analysis and Potential Theory to analyse domain perturbation problems for boundary value problems for nonhomogeneous elliptic equations. We consider the Dirichlet problem for the Poisson equation and show theorems of real analytic dependence upon domain perturbation for the solutions and for the corresponding energy integrals both for the case wherein the data in the interior are real analytic and for the case wherein the data in the interior are derivatives of Hölder continuous functions.

Keywords:

• Dirichlet boundary value problem
• Poisson equation
• Domain perturbation
• 2000 Mathematics Subject Classifications: 35J25
• 31B10
• 45F15
• 47H30

Notes

This article is dedicated to the 65th birthday of Prof. Heinrich Begehr, with a wish for many happy and scientifically fruitful years to come.

Additional information

Notes on contributors

Massimo Lanza de Cristoforis

This article is dedicated to the 65th birthday of Prof. Heinrich Begehr, with a wish for many happy and scientifically fruitful years to come.