Ergodicity and local limits for stochastic local and nonlocal pLaplace equations
Abstract
Ergodicity for local and nonlocal stochastic singular $p$Laplace equations is proven, without restriction on the spatial dimension and for all $p\in[1,2)$. This generalizes previous results from [Gess, Tölle; J. Math. Pures Appl., 2014], [Liu, Tölle; Electron. Commun. Probab., 2011], [Liu; J. Evol. Equations, 2009]. In particular, the results include the multivalued case of the stochastic (nonlocal) total variation flow, which solves an open problem raised in [Barbu, Da Prato, Röckner; SIAM J. Math. Anal., 2009]. Moreover, under appropriate rescaling, the convergence of the unique invariant measure for the nonlocal stochastic $p$Laplace equation to the unique invariant measure of the local stochastic $p$Laplace equation is proven.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 DOI:
 10.48550/arXiv.1507.04545
 arXiv:
 arXiv:1507.04545
 Bibcode:
 2015arXiv150704545G
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs;
 Primary: 35K55;
 35K92;
 60H15;
 Secondary: 37L15;
 45E10
 EPrint:
 30 pages