Ergodicity and local limits for stochastic local and nonlocal p-Laplace 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 e-prints
- 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
- E-Print:
- 30 pages