Maximum principle for non-uniformly parabolic equations and applications
Analysis of PDEs
2021-05-18 v2 Probability
Abstract
In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion and drift coefficients. Moreover, by the Markov selection theorem of Krylov [8], we also establish the existence of the associated strong Markov family.
Cite
@article{arxiv.2012.05026,
title = {Maximum principle for non-uniformly parabolic equations and applications},
author = {Xicheng Zhang},
journal= {arXiv preprint arXiv:2012.05026},
year = {2021}
}
Comments
30pages