Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise

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Details

Original languageEnglish
Pages (from-to)1764–1792
Number of pages29
JournalJournal of Functional Analysis
Volume271
Issue number7
Publication statusPublished - Oct 2016
MoE publication typeA1 Journal article-refereed

Researchers

  • Ioana Ciotir
  • Jonas Tölle

Research units

  • INSA Rouen

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].

ID: 4440147