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- W4287906172 abstract "In this note, we prove a uniqueness result, up to a positive multiplicative constant, for nontrivial convex solutions to a system of Monge-Amp`ere equations begin{equation*} left{ begin{alignedat}{2} det D^2 u~& = gamma |v|^p~&&text{in} ~ Omega, det D^2 v~& = mu |u|^{n^2/p}~&&text{in} ~ Omega, u=v &= 0~&&text{on}~ partialOmega end{alignedat} right. end{equation*} on bounded, smooth and uniformly convex domains $Omegasubset R^n$ provided that $p$ is close to $ngeq 2$. When $p=n$, we show that the uniqueness holds for general bounded convex domains $Omegasubset R^n$." @default.
- W4287906172 created "2022-07-26" @default.
- W4287906172 creator A5027907644 @default.
- W4287906172 date "2020-01-07" @default.
- W4287906172 modified "2023-09-28" @default.
- W4287906172 title "Uniqueness for a system of Monge-Amp`ere equations" @default.
- W4287906172 doi "https://doi.org/10.48550/arxiv.2001.02196" @default.
- W4287906172 hasPublicationYear "2020" @default.
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