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

Wei Zhou

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

Analysis of PDEs 2013-11-26 v1 Complex Variables Differential Geometry

Authors: Wei Zhou

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.

Keywords

dirichlet problem regularity for elliptic equations regularity theory

Cite

@article{arxiv.1311.6450,
  title  = {Representation and regularity for the Dirichlet problem for real and complex degenerate Hessian equations},
  author = {Wei Zhou},
  journal= {arXiv preprint arXiv:1311.6450},
  year   = {2013}
}

Comments

42 pages. Comments are welcome

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