English

A viscosity approach to the Dirichlet problem for degenerate complex Hessian type equations

Complex Variables 2018-10-10 v1 Analysis of PDEs

Abstract

A viscosity approach is introduced for the Dirichlet problem associated to complex Hessian type equations on domains in \Cn\C^n. The arguments are modelled on the theory of viscosity solutions for real Hessian type equations developed by Trudinger. As consequence we solve the Dirichlet problem for the Hessian quotient and special Lagrangian equations. We also establish basic regularity results for the solutions.

Keywords

Cite

@article{arxiv.1712.08572,
  title  = {A viscosity approach to the Dirichlet problem for degenerate complex Hessian type equations},
  author = {Slawomir Dinew and Hoang-Son Do and Tat Dat To},
  journal= {arXiv preprint arXiv:1712.08572},
  year   = {2018}
}

Comments

29 pages

R2 v1 2026-06-22T23:27:39.057Z