English

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.

Keywords

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

R2 v1 2026-06-23T20:50:37.564Z