Communications on Pure and Applied Analysis (CPAA)

Multi-valued solutions to a class of parabolic Monge-Ampère equations

Pages: 1061 - 1074, Volume 13, Issue 3, May 2014      doi:10.3934/cpaa.2014.13.1061

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Limei Dai - School of Mathematics and information Science, Weifang University, Shandong Weifang, 261061, China (email)

Abstract: In this paper, we investigate the multi-valued solutions of a class of parabolic Monge-Ampère equation $-u_{t}\det(D^{2}u)=f$. Using the Perron method, we obtain the existence of finitely valued and infinitely valued solutions to the parabolic Monge-Ampère equations. We generalize the results of elliptic Monge-Ampère equations and Hessian equations.

Keywords:  Parabolic Monge-Ampère equations, multi-valued solutions, Perron method, viscosity solutions, existence.
Mathematics Subject Classification:  Primary: 35K96, 35D40.

Received: March 2013;      Revised: September 2013;      Available Online: December 2013.