In this paper, we consider an approach based on Functional Analysis and Potential Theory to analyze singular domain perturbation problems for boundary value problems for nonhomogeneous elliptic equations. This paper can be considered as a continuation of [\refcite{La04b}], [\refcite{La04c}], where we have considered the case of homogeneous equations. For simplicity, we confine our attention to the Poisson equation, and to Dirichlet boundary conditions.
A singular domain perturbation problem for the Poisson equation
LANZA DE CRISTOFORIS, MASSIMO
2009
Abstract
In this paper, we consider an approach based on Functional Analysis and Potential Theory to analyze singular domain perturbation problems for boundary value problems for nonhomogeneous elliptic equations. This paper can be considered as a continuation of [\refcite{La04b}], [\refcite{La04c}], where we have considered the case of homogeneous equations. For simplicity, we confine our attention to the Poisson equation, and to Dirichlet boundary conditions.
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