Coupling Levy measures and comparison principles for viscosity solutions
Analysis of PDEs
2019-04-23 v2
Abstract
We prove new comparison principles for viscosity solutions of non-linear integro-differential equations. The operators to which the method applies include but are not limited to those of L\'evy-It\^o type. The main idea is to use an optimal transport map to couple two different L\'evy measures, and use the resulting coupling in a doubling of variables argument
Cite
@article{arxiv.1805.06955,
title = {Coupling Levy measures and comparison principles for viscosity solutions},
author = {Nestor Guillen and Chenchen Mou and Andrzej Swiech},
journal= {arXiv preprint arXiv:1805.06955},
year = {2019}
}
Comments
39 pages, no figures, added a new section discussing several examples and clarified and corrected some of the proofs related to the background material in the appendix, to appear in Transactions of the American Mathematical Society