$C^{1,1}$ Solution of the Dirichlet Problem for Degenerate $k$-Hessian Equations

Abstract

In this paper, we prove the existence of $C^{1,1}$-solution to the Dirichlet problem for degenerate elliptic $k$-Hessian equations $S_k[u]=f$ under a condition which is weaker than the condition $f^{1/k}\in C^{1,1}(\bar{\Omega })$.

18pages

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