A variational approach to dissipative SPDEs with singular drift

DOI10.1214/17-AOP1207zbMath1454.60097arXiv1604.08808MaRDI QIDQ1647734

Carlo Marinelli, Luca Scarpa

Publication date: 26 June 2018

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08808

zbMATH Keywords

well-posednessvariational approachmonotone operatorsmultiplicative noisestochastic evolution equationssingular drift

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Applications of functional analysis in probability theory and statistics (46N30)

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Cites Work

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• Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations
• On smoothing properties of transition semigroups associated to a class of SDEs with jumps
• Stochastic partial differential equations: an introduction
• Existence for semilinear parabolic stochastic equations
• Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions
• Kolmogorov equations for stochastic PDEs.
• Convexity inequalities for positive operators
• Stochastic evolution equations in UMD Banach spaces
• Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
• Semigroups of linear operators and applications to partial differential equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term
• Stochastic nonlinear beam equations
• Analysis and control of nonlinear infinite dimensional systems
• Perturbation theory for linear operators.
• Stochastic differential equations, backward SDEs, partial differential equations
• On continuity of functions with values in various Banach spaces
• Existence of Weak Solutions for a Class of Semilinear Stochastic Wave Equations
• Nash type inequalities for fractional powers of non-negative self-adjoint operators
• STRONG SOLUTIONS FOR STOCHASTIC POROUS MEDIA EQUATIONS WITH JUMPS
• One-Parameter Semigroups for Linear Evolution Equations
• Integral representations of resolvents and semigroups
• On Well-Posedness of Semilinear Stochastic Evolution Equations on $L_p$ Spaces
• $$ W_0^{1,1} $$ Solutions in Some Borderline Cases of Elliptic Equations with Degenerate Coercivity