Gradient Estimates for Nonlinear Diffusion Semigroups by Coupling Methods
Probability
2014-07-22 v1
Abstract
Our purpose is to obtain gradient estimates for certain nonlinear partial differential equations by coupling methods. First we derive uniform gradient estimates for a certain semi-linear PDEs based on the coupling method introduced in Wang (2011) and the theory of backward SDEs. Then we generalize Wang's coupling to the -expectation space and obtain gradient estimates for nonlinear diffusion semigroups, which correspond to the solutions of a certain fully nonlinear PDEs.
Cite
@article{arxiv.1407.5426,
title = {Gradient Estimates for Nonlinear Diffusion Semigroups by Coupling Methods},
author = {Yongsheng Song},
journal= {arXiv preprint arXiv:1407.5426},
year = {2014}
}
Comments
19 pages