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 \(f \equiv 1\).
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Received: 4 February 2003, Accepted: 3 March 2004, Published online: 16 July 2004
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Savin, O. The obstacle problem for Monge Ampere equation. Calc. Var. 22, 303–320 (2005). https://doi.org/10.1007/s00526-004-0275-8
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DOI: https://doi.org/10.1007/s00526-004-0275-8