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Bounded Pointwise Approximation of Solutions of Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

A. Bonilla  and
R. Trujillo-González
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 ℝN 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.

Keywords

35A3541A3035J3031B15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 3 , 01 June 1996 , pp. 496 - 511
Copyright
Copyright © Canadian Mathematical Society 1996

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