Symmetry of solutions to a class of Monge-Ampère equations

Fan Cui; Huaiyu Jian

doi:10.3934/cpaa.2019060

Article Contents

2019, Volume 18, Issue 3: 1247-1259. Doi: 10.3934/cpaa.2019060

This issue Previous Article Reaction of the fluid flow on time-dependent boundary perturbation Next Article Ground states of nonlinear Schrödinger systems with periodic or non-periodic potentials

Symmetry of solutions to a class of Monge-Ampère equations

Fan Cui and
Huaiyu Jian^,

Department of Mathematics, Tsinghua University, Beijing 100084, China

Received: March 31, 2018

Revised: March 31, 2018

Published: May 2019

The second author is supported by NSFC 11771237 and 41390452

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Abstract

We study the symmetry of solutions to a class of Monge-Ampère type equations from a few geometric problems. We use a new transform to analyze the asymptotic behavior of the solutions near the infinity. By this and a moving plane method, we prove the radially symmetry of the solutions.

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Mathematics Subject Classification: Primary: 35J60, 53A15; Secondary: 35J60, 35J96, 53A15.

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