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

@article{Ciotir2016NonlinearSP,
  title={Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise},
  author={Ioana Ciotir and Jonas M. Tolle},
  journal={Journal of Functional Analysis},
  year={2016},
  volume={271},
  pages={1764-1792}
}
  • Ioana Ciotir, Jonas M. Tolle
  • Published 2016
  • Mathematics
  • Journal of Functional Analysis
  • 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… CONTINUE READING

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