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arXiv · 1205.5934

Fully Degenerate Monge Amp\'ere Equations

Panagiota Daskalopoulos·Ki-ahm Lee
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Abstract

In this paper, we consider the following nonlinear eigenvalue problem for the Monge-Amp\'ere equation: find a non-negative weakly convex classical solution $f$ satisfying {equation*} {cases} \det D^2 f=f^p \quad &\text{in $\Omega$} f=\vp \quad &text{on $\partial\Omega$} {cases} {equation*} for a strictly convex smooth domain $\Omega\subset\R^2$ and $0 0\}}$ and whose free boundary $\partial\{f=0\}$ is also smooth.

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Panagiota Daskalopoulos, Ki-ahm Lee. 2012-05-27. Fully Degenerate Monge Amp\'ere Equations. https://arxiv.org/abs/1205.5934

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