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The Dirichlet problem for degenerate elliptic 2-dimensional Monge-Ampère equation

Published online by Cambridge University Press:  17 April 2009

Kazuo Amano
Kazuo Amano
Affiliation:
Centre for Mathematical Analysis, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia
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Abstract

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We study the following Dirichlet problem for the degenerate elliptic Monge-Ampère equation: Given , f ≥ 0 and , find a solution , t ≥ 2, satisfying in Ω and u = g on ∂Ω. Since f is nonnegative, we cannot apply any standard elliptic methods. In this paper, we use an iteration scheme of Nash-Moser type and a priori estimates for degenerate elliptic operators, and solve the Dirichlet problem for a certain class of f and g.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 389 - 410
Copyright
Copyright © Australian Mathematical Society 1988

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