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

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  • Tölle, Jonas M.

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.

Suggested Citation

  • Tölle, Jonas M., 2020. "Stochastic evolution equations with singular drift and gradient noise via curvature and commutation conditions," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3220-3248.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:3220-3248
    DOI: 10.1016/j.spa.2019.09.011
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    References listed on IDEAS

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    1. Ciotir, Ioana & Tölle, Jonas M., 2012. "Convergence of invariant measures for singular stochastic diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1998-2017.
    2. Barbu, Viorel & Brzeźniak, Zdzisław & Hausenblas, Erika & Tubaro, Luciano, 2013. "Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 934-951.
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