Well-posedness and regularity for distribution dependent SPDEs with singular drifts

被引：15

作者：

Huang, Xing ^{[1
]}

Song, Yulin ^{[2
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 203卷

关键词：

Cylindrical Brownian motion; Relative entropy; Dini continuous; Distribution dependent; Harnack inequality; LOG-HARNACK INEQUALITY; EQUATIONS; SDES;

D O I：

10.1016/j.na.2020.112167

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the distribution dependent stochastic differential equation in a separable Hilbert space with a Dini continuous drift is investigated. The existence and uniqueness of weak and strong solutions are obtained. Moreover, some regularity results as well as gradient estimates and Wang's log-Harnack inequality are derived for the associated semigroup. In addition, Wang's Harnack inequality with power and shift Harnack inequality are also proved when the noise is additive. All of the results extend the ones in the distribution independent situation. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：18

共 32 条

[1] A semilinear Mckean-Vlasov stochastic evolution equation in Hilbert space [J].

Ahmed, NU ;

Ding, X .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 60 (01) :65-85

[2]

[Anonymous], 1974, Math. USSR Sb.

[3]

Barbu V., ARXIV180810706

[4] PROBABILISTIC REPRESENTATION FOR SOLUTIONS TO NONLINEAR FOKKER-PLANCK EQUATIONS [J].

Barbu, Viorel ;

Roeckner, Michael .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2018, 50 (04) :4246-4260

[5]

Bauer M., ARXIV191207427

[6]

Bauer M., ARXIV191205932

[7]

Bauer M., ARXIV180611451

[8] Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces [J].

Brzezniak, Z ;

Gatarek, D .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 84 (02) :187-225

[9] N-PLAYER GAMES AND MEAN-FIELD GAMES WITH ABSORPTION [J].

Campi, Luciano ;

Fischer, Markus .

ANNALS OF APPLIED PROBABILITY, 2018, 28 (04) :2188-2242

[10]

Chaudru de Raynal P.E., 2019, STRONG WELL POSEDNES, DOI [10.1016/j.spa.2019.01.006, DOI 10.1016/J.SPA.2019.01.006]

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