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 -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.
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}
}