English

The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation

Analysis of PDEs 2023-01-13 v1

Abstract

In this paper, we consider the homogeneous complex k-Hessian equation in an exterior domain CnΩ\mathbb{C}^n\setminus\Omega. We prove the existence and uniqueness of the C1,1C^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second order estimate.

Keywords

Cite

@article{arxiv.2208.03794,
  title  = {The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation},
  author = {Zhenghuan Gao and Xi-Nan Ma and Dekai Zhang},
  journal= {arXiv preprint arXiv:2208.03794},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2207.13504

R2 v1 2026-06-25T01:33:05.245Z