An interior estimate for convex solutions and a rigidity theorem

Published 6 Apr 2015 in math.AP | (1504.01206v1)

Abstract: We establish an interior $C^2$ estimate for $k+1$ convex solutions to Dirichlet problems of $k$-Hessian equations. We also use such estimate to obtain a rigidity theorem for $k+1$ convex entire solutions of $k$-Hessian equations in Euclidean space.

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