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

Heming Jiao; Zhizhang Wang

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

Analysis of PDEs 2022-06-03 v1

Authors: Heming Jiao , Zhizhang Wang

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.

Keywords

k-hessian equation degenerate equation convex solution second order estimate dirichlet problem c1,1 estimate

Cite

@article{arxiv.2206.00834,
  title  = {Second order estimates for convex solutions of degenerate $k$-Hessian equations},
  author = {Heming Jiao and Zhizhang Wang},
  journal= {arXiv preprint arXiv:2206.00834},
  year   = {2022}
}

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