English

Uniform $L^\infty$ estimates: subsolutions to fully nonlinear partial differential equations

Analysis of PDEs 2024-01-23 v1 Differential Geometry

Abstract

Uniform bounds are obtained using the auxiliary Monge-Amp\`ere equation method for solutions of very general classes of fully non-linear partial differential equations, assuming the existence of a C{C}-subsolution in the sense of G. Sz\'ekelyhidi and B. Guan. The main advantage over previous estimates is in the K\"ahler case, where the new estimates remain uniform as the background metric is allowed to degenerate.

Keywords

Cite

@article{arxiv.2401.11572,
  title  = {Uniform $L^\infty$ estimates: subsolutions to fully nonlinear partial differential equations},
  author = {Bin Guo and Duong H. Phong},
  journal= {arXiv preprint arXiv:2401.11572},
  year   = {2024}
}
R2 v1 2026-06-28T14:22:58.182Z