A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity.(English)Zbl 0704.35045

The author considers viscosity solutions of the Monge-Ampère equation $(1)\quad 0<\lambda_ 1\leq \det D^ 2u\leq \lambda_ 2$ with $$C^{1,\alpha}$$ boundary data $$(\alpha >1-2/n)$$. Assume that $$u\geq 0$$ satisfies (1) and that the convex set $$\{u=0\}$$ is not a point. Then this set cannot have extremal points in the interior of the domain of definition of u.
Reviewer: G.Dziuk

MSC:

 35J60 Nonlinear elliptic equations 35B50 Maximum principles in context of PDEs
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