Liouville theorems for a class of degenerate or singular Monge-Amp\`ere equations
Analysis of PDEs
2023-04-25 v1
Abstract
In this note, we classify solutions to a class of Monge-Amp\`ere equations whose right hand side may be degenerate or singular in the half space. Solutions to these equations are special solutions to a class of fourth order equations, including the affine maximal hypersurface equation, in the half space. Both the Dirichlet boundary value and Neumann boundary value cases are considered.
Keywords
Cite
@article{arxiv.2304.12060,
title = {Liouville theorems for a class of degenerate or singular Monge-Amp\`ere equations},
author = {Ling Wang and Bin Zhou},
journal= {arXiv preprint arXiv:2304.12060},
year = {2023}
}
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14 pages