Global H\"older estimates for 2D linearized Monge-Amp\`ere equations with right-hand side in divergence form
Analysis of PDEs
2019-02-22 v1
Abstract
We establish global H\"older estimates for solutions to inhomogeneous linearized Monge-Amp\`ere equations in two dimensions with the right hand side being the divergence of a bounded vector field. These equations arise in the semi-geostrophic equations in meteorology and in the approximation of convex functionals subject to a convexity constraint using fourth order Abreu type equations. Our estimates hold under natural assumptions on the domain, boundary data and Monge-Amp\`ere measure being bounded away from zero and infinity. They are an affine invariant and degenerate version of global H\"older estimates by Murthy-Stampacchia and Trudinger for second order elliptic equations in divergence form.
Keywords
Cite
@article{arxiv.1902.08113,
title = {Global H\"older estimates for 2D linearized Monge-Amp\`ere equations with right-hand side in divergence form},
author = {Nam Q. Le},
journal= {arXiv preprint arXiv:1902.08113},
year = {2019}
}