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The Dirichlet problem for degenerate elliptic 2-dimensional Monge-Ampère equation
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1988
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