English

Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Amp\`ere equation

Analysis of PDEs 2020-11-04 v2 Complex Variables

Abstract

We prove sharp uniform estimates for strong supersolutions of a large class of fully nonlinear degenerate elliptic complex equations. Our findings rely on ideas of Kuo and Trudinger who dealt with degenerate linear equations in the real setting. We also exploit the pluripotential theory for the complex Monge-Amp\`ere operator as well as suitably tailored theory of LpL^p-viscosity subsolutions.

Keywords

Cite

@article{arxiv.2010.08434,
  title  = {Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Amp\`ere equation},
  author = {Soufian Abja and Sławomir Dinew and Guillaume Olive},
  journal= {arXiv preprint arXiv:2010.08434},
  year   = {2020}
}