Semiconcavity of viscosity solutions for a class of degenerate elliptic integro-differential equations in $\mathbb R^n$

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Abstract

This paper is concerned with semiconcavity of viscosity solutions for a class of degenerate elliptic integro-differential equations in $\mathbb R^n$. This class of equations includes Bellman equations containing operators of L\'evy-It\^o type. H\"{o}lder and Lipschitz continuity of viscosity solutions for a more general class of degenerate elliptic integro-differential equations are also provided.