A maximum rank problem for degenerate elliptic fully nonlinear equations

Details A maximum rank problem for degenerate elliptic fully nonlinear equations A maximum rank problem for degenerate elliptic fully nonlinear equations

2010-09-21

arxiv.org/abs/1009.3975v2

Mathematics

Analysis of PDEs

Scientific paper

The solutions to the Dirichlet problem for two degenerate elliptic fully
nonlinear equations in $n+1$ dimensions, namely the real Monge-Amp\`ere
equation and the Donaldson equation, are shown to have maximum rank in the
space variables when $n \leq 2$. A constant rank property is also established
for the Donaldson equation when $n=3$.

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