On the viscosity approach to a class of fully nonlinear elliptic equations
Abstract
In this paper, we study some properties of viscosity sub/super-solutions of a class of fully nonlinear elliptic equations relative to the eigenvalues of the complex Hessian. We show that every viscosity subsolution is approximated by a decreasing sequence of smooth subsolutions. When the equations satisfy some conditions on the limit at infinity, we verify that the comparison principle holds, and as a sequence, we obtain a result about the existence of solution of the Dirichlet problem. Using the comparison principle, we show that, under suitable conditions, a Perron-Bremermann envelope can be approximated by a decreasing sequence of viscosity solutions.
Keywords
Cite
@article{arxiv.2102.12744,
title = {On the viscosity approach to a class of fully nonlinear elliptic equations},
author = {Hoang-Son Do and Quang Dieu Nguyen},
journal= {arXiv preprint arXiv:2102.12744},
year = {2021}
}
Comments
13 pages; In this version, we made some changes to Theorem 1.4 and fixed some minor errors