Harnack's inequality for solutions to the linearized Monge-Ampere equation under minimal geometric assumptions

Diego Maldonado

Harnack's inequality for solutions to the linearized Monge-Ampere equation under minimal geometric assumptions

Analysis of PDEs 2012-03-19 v2 Classical Analysis and ODEs

Authors: Diego Maldonado

Abstract

We prove a Harnack inequality for solutions to $L_A u = 0$ where the elliptic matrix $A$ is adapted to a convex function satisfying minimal geometric conditions. An application to Sobolev inequalities is included.

Keywords

Harnack inequality linearized Monge-Ampère equation convex function elliptic matrix Sobolev inequality

Cite

@article{arxiv.1110.5263,
  title  = {Harnack's inequality for solutions to the linearized Monge-Ampere equation under minimal geometric assumptions},
  author = {Diego Maldonado},
  journal= {arXiv preprint arXiv:1110.5263},
  year   = {2012}
}

Comments

A claim after equation (2.12) is unsubstantiated. I'm withdrawing the manuscript until I figure out if I can fix it. The main application to Sobolev inequalities should still hold true. I thank Truyen Van Nguyen for pointing out this error

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