Estimates for Nonlinear Stochastic Partial Differential Equations with Gradient Noise via Dirichlet Forms

被引：3

作者：

Toelle, Jonas M. ^{[1
]}

机构：

[1] Univ Augsburg, Inst Math, D-86135 Augsburg, Germany

来源：

STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND RELATED FIELDS: IN HONOR OF MICHAEL ROCKNER, SPDERF | 2018年 / 229卷

关键词：

Nonlinear stochastic partial differential equations; Dirichlet forms; A Priori estimate; Stochastic p-laplace evolution equation; Gradient Stratonovich noise; Commutator bound; Bakry-Emery curvature-dimension condition; VARIATIONAL-INEQUALITIES; FLOW;

D O I：

10.1007/978-3-319-74929-7_14

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a priori estimates for nonlinear Stratonovich stochastic partial differential equations on the d-dimensional torus with p-Laplace-type drift with sublinear non-homogeneous nonlinearities and Gaussian gradient Stratonovich noise with C-1-vector field coefficients. Assuming a commutator bound, the results are obtained by using resolvent and Dirichlet form methods and an approximative Itoformula.

引用

页码：249 / 262

页数：14

共 26 条

[1] BAKRY-EMERY CURVATURE-DIMENSION CONDITION AND RIEMANNIAN RICCI CURVATURE BOUNDS [J].

Ambrsio, Luigi ;

Gigli, Nicola ;

Savare, Giuseppe .

ANNALS OF PROBABILITY, 2015, 43 (01) :339-404

[2]

[Anonymous], 2009, AMSIP STUDIES ADV MA

[3]

[Anonymous], 1984, Applicable mathematics series

[4]

[Anonymous], 2007, Linear Algebra and its Applications

[5]

[Anonymous], PURE APPL MATH

[6]

Bakry D, 1997, NEW TRENDS IN STOCHASTIC ANALYSIS, P43

[7]

Bakry D., 2014, Analysis and geometry of Markov diffusion operators, Grundlehren der mathematischen Wissenschaften Fundamental Principles of Mathematical Sciences, V348

[8]

Barbu V., 2017, Appl. Math. Optim., V188, P1

[9] An operatorial approach to stochastic partial differential equations driven by linear multiplicative noise [J].

Barbu, Viorel ;

Roeckner, Michael .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2015, 17 (07) :1789-1815

[10] Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise [J].

Barbu, Viorel ;

Roeckner, Michael .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 209 (03) :797-834

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