Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589557 | Journal of Functional Analysis | 2016 | 29 Pages |
Abstract
We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative Stratonovich gradient-type noise. We derive a commutator relation for the unbounded noise coefficients in terms of a geometric Killing vector condition. The drift term is given by the total variation flow, respectively, by a singular p-Laplace-type operator. We impose nonlinear zero Neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise. This solves an open problem posed in Barbu et al. (2013) [7] and Barbu and Röckner (2015) [10].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ioana Ciotir, Jonas M. Tölle,