Second order estimates for convex solutions of degenerate $k$-Hessian equations

Heming Jiao; Zhizhang Wang

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arXiv · 2206.00834

Second order estimates for convex solutions of degenerate $k$-Hessian equations

Heming Jiao·Zhizhang Wang

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Abstract

The $C^{1,1}$ estimate of the Dirichlet problem for degenerate $k$-Hessian equations with non-homogenous boundary conditions is an open problem, if the right hand side function $f$ is only assumed to satisfy $f^{1/(k-1)} \in C^{1,1}$. In this paper, we solve this problem for convex solutions defined in the strictly convex bounded domain.

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BibTeX RIS

Heming Jiao, Zhizhang Wang. 2022-06-02. Second order estimates for convex solutions of degenerate $k$-Hessian equations. https://arxiv.org/abs/2206.00834

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