Symmetry of solutions to parabolic Monge-Ampère equations
School of Mathematics and Information Science, Weifang University, Weifang, Shandong, 261061, China
Boundary Value Problems 2013, 2013:185 doi:10.1186/1687-2770-2013-185Published: 20 August 2013
In this paper, we study the parabolic Monge-Ampère equation
Using the method of moving planes, we show that any parabolically convex solution is symmetric with respect to some hyperplane. We also give a counterexample in and an example in a cylinder to illustrate the results.
MSC: 35K96, 35B06.