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

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

Received: March 2010

Revised: April 2010

Published: September 2010

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Abstract

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

$ L_$φ$ u$:$=\sum $φ^ij$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 $\infty$.

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Mathematics Subject Classification: Primary: 35J70, 35B65.

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