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

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 $C^{1}$-vector field 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 It\^o-formula.
 Comments: 25 pages, 53 references Subjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA); Probability (math.PR) MSC classes: Primary: 35K55, 35K92, 60H15, Secondary: 49J40, 58J65 Cite as: arXiv:1803.07005 [math.AP] (or arXiv:1803.07005v1 [math.AP] for this version)

## Submission history

From: Jonas M. Tölle Dr. math. [view email]
[v1] Mon, 19 Mar 2018 15:59:03 GMT (26kb)