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arXiv · 1311.6450

Representation and regularity for the Dirichlet problem for real and complex degenerate Hessian equations

Wei Zhou
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Abstract

We consider the Dirichlet problem for positively homogeneous, degenerate elliptic, concave (or convex) Hessian equations. Under natural and necessary conditions on the geometry of the domain, with the $C^{1,1}$ boundary data, we establish the interior $C^{1,1}$-regularity of the unique (admissible) solution, which is optimal even if the boundary data is smooth. Both real and complex cases are studied by the unified (Bellman equation) approach.

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Wei Zhou. 2013-11-25. Representation and regularity for the Dirichlet problem for real and complex degenerate Hessian equations. https://arxiv.org/abs/1311.6450

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