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arXiv · 1803.07005

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

Jonas M. Tölle
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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 It\^{o}-formula.

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Jonas M. Tölle. 2018-03-19. Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions. https://doi.org/10.1016/j.spa.2019.09.011

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