Maximum principle for non-uniformly parabolic equations and applications

2020/12/09 by Xicheng Zhang, Zhang, Xicheng
Computer Science · Economics, Econometrics and Finance · Mathematics · #35K10 #60H10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2012.05026

openalex publication_date 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On time inhomogeneous stochastic Itô equations with drift in L_d+1

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