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The second-order parabolic PDEs with singular coefficients and applications
Stochastic Analysis and Applications ( IF 1.3 ) Pub Date : 2020-05-26 , DOI: 10.1080/07362994.2020.1766983
Rongrong Tian 1, 2 , Jinlong Wei 3 , Yanbin Tang 1
Affiliation  

Abstract The goal of this paper is to establish the Lipschitz and estimates for a second-order parabolic PDE on with zero initial data and f satisfying a Ladyzhenskaya–Prodi–Serrin type condition. Following the theoretic result, we then give two applications. The first is to discuss the regularity of the stochastic heat equations, and the second is to discuss the Sobolev differentiability of strong solutions to a class of SDEs with singular drift coefficients.

中文翻译:

具有奇异系数的二阶抛物线偏微分方程及其应用

摘要 本文的目标是在零初始数据和满足 Ladyzhenskaya-Prodi-Serrin 类型条件的 f 上建立 Lipschitz 和二阶抛物线偏微分方程的估计。根据理论结果,我们再给出两个应用。第一个是讨论随机热方程的正则性,第二个是讨论一类具有奇异漂移系数的SDEs强解的Sobolev可微性。
更新日期:2020-05-26
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