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Smoothing the domain out for positive solutions

Published online by Cambridge University Press:  17 April 2009

Yaping Liu
Yaping Liu
Affiliation:
Department of Mathematics, Pittsburg State University, Pittsburg KS 66762-7500, United States of America
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Abstract

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For a given nonlinear partial differential equation defined on a bounded domain with irregular boundary, the available analytical tools are very limited in relation to the study of positive solutions. In this paper wer first use weak convergence methods to show that for an elliptic equation of a certain type, classical positive solutions on nearby smooth domains approach a generalised positive solution on the given domain. The idea is then applied to sublinear elliptic problems to obtain existence and uniqueness results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 405 - 413
Copyright
Copyright © Australian Mathematical Society 2000

References

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