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

Chao-Jiang Xu; Qi Wang

arxiv: 1309.4204 · v1 · pith:KGN7KRWEnew · submitted 2013-09-17 · 🧮 math.AP

C^(1, 1) Solution of the Dirichlet Problem for Degenerate k-Hessian Equations

Qi Wang , Chao-Jiang Xu This is my paper

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keywords conditiondegeneratedirichletequationshessianproblemsolutionelliptic

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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 $f^{1/k}\in C^{1,1}(\bar\Omega)$.

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C^(1, 1) Solution of the Dirichlet Problem for Degenerate k-Hessian Equations

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