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

Qi Wang, Chao-Jiang Xu

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 th…