Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions

Jonas M. Tölle

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 3220-3248

Abstract: We prove existence and uniqueness of solutions to a nonlinear stochastic evolution equation on the d-dimensional torus with singular p-Laplace-type or total variation flow-type drift with general sublinear doubling nonlinearities and Gaussian gradient Stratonovich noise with divergence-free coefficients. Assuming a weak defective commutator bound and a curvature-dimension condition, the well-posedness result is obtained in a stochastic variational inequality setup by using resolvent and Dirichlet form methods and an approximative Itô-formula.

Keywords: Nonlinear Stratonovich stochastic partial differential equation; Stochastic variational inequality; Singular stochastic p-Laplace evolution equation; Multiplicative gradient Stratonovich noise; Defective commutator bound; Bakry-Émery curvature-dimension condition (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.09.011

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