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The obstacle problem for Monge Ampere equation

Authors:	Ovidiu Savin

Institution:	(1) Department of Mathematics, UC Berkeley, CA 94720 Berkeley, USA

Abstract:	We consider the following obstacle problem for Monge-Ampere equation $\det D^2 u = f \chi_{\{u > 0\}}$ and discuss the regularity of the free boundary $\partial \{u = 0 \}$ . We prove that $\partial \{u = 0 \}$ is $C^{1,\alpha}$ if f is bounded away from 0 and $\infty$ , and it is C ^1,1 if $f \equiv 1$ .Received: 4 February 2003, Accepted: 3 March 2004, Published online: 16 July 2004

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