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Fully Nonlinear Elliptic Equations on General Domains

Published online by Cambridge University Press:  20 November 2018

Jiguang Bao
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Abstract

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By means of the Pucci operator, we construct a function ${{u}_{0}}$, which plays an essential role in our considerations, and give the existence and regularity theorems for the bounded viscosity solutions of the generalized Dirichlet problems of second order fully nonlinear elliptic equations on the general bounded domains, which may be irregular. The approximation method, the accretive operator technique and the Caffarelli's perturbation theory are used.

Keywords

35D0535D1035J6035J67Pucci operatorviscosity solutionexistenceC2,ψ regularityDini conditionfully nonlinear equationgeneral domainaccretive operatorapproximation lemma
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 6 , 01 December 2002 , pp. 1121 - 1141
Copyright
Copyright © Canadian Mathematical Society 2002

Footnotes

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Permanent address: Department of Mathematics, Beijing Normal University, Beijing, 100875, People's Republic of China e-mail: [email protected]

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