July  2010, 28(3): 865-873. doi: 10.3934/dcds.2010.28.865

A Liouville theorem for solutions to the linearized Monge-Ampere equation

1. 

Department of Mathematics, Columbia University, Columbia University, New York, NY 10027, United States

Received  March 2010 Revised  April 2010 Published  April 2010

We prove that global Lipschitz solutions to the linearized Monge-Ampere equation

$ L_$φ$ u$:$=\sum $φij$u_{ij}=0$

must be linear in $2D$. The function φ is assumed to have the Monge-Ampere measure $\det D^2 $φ bounded away from $0$ and $\infty$.

Citation: Ovidiu Savin. A Liouville theorem for solutions to the linearized Monge-Ampere equation. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 865-873. doi: 10.3934/dcds.2010.28.865
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