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Convergence of invariant measures for singular stochastic diffusion equations

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  • Ciotir, Ioana
  • Tölle, Jonas M.

Abstract

It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:4:p:1998-2017
    DOI: 10.1016/j.spa.2011.11.011
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    References listed on IDEAS

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    1. Barbu, Viorel & Da Prato, Giuseppe, 2010. "Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1247-1266, July.
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    Cited by:

    1. 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.

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