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Bounded Pointwise Approximation of Solutions of Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

A. Bonilla
Affiliation:
Departamento de Análisis Matemático Universidad de La Laguna 38271 La Laguna, Tenerife Spain
R. Trujillo-González
Affiliation:
Departamento de Análisis Matemático Universidad de La Laguna 38271 La Laguna, Tenerife Spain
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Abstract

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We characterize open subsets U of N in which the bounded solutions of certain elliptic equations can be approximated pointwise by uniformly bounded solutions that are continuous in Ū. This result is established in terms of certain capacities. For closed subsets X, this characterization allows us to approximate bounded solutions in X° uniformly on relatively closed subsets of X° by solutions continuous on certain subsets of the boundary of X.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1996

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