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Convergence of approximate solutions of a quasilinear partial differential equation

Published online by Cambridge University Press:  17 April 2009

T.R. Cranny
T.R. Cranny
Affiliation:
Department of MathematicsThe University of QueenslandQueensland 4072Australia
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Abstract

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This article is a sequel to a paper in which a quasilinear partial differential equation with nonlinear boundary condition was approximated using mollifiers, and the existence of solutions to the approximating problem shown under quite general conditions. In this paper we show that standard a priori Hölder estimates ensure the convergence of these solutions to a classical solution of the original problem. Some partial results giving such estimates for special cases are described.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 3 , December 1994 , pp. 425 - 433
Copyright
Copyright © Australian Mathematical Society 1994

References

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