arXiv 1507.045452015-07math.PRmath.AP

Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations

Benjamin Gess, Jonas M. Tölle

备注：: 30 pages; to appear in SIAM J. Math. Anal
发表信息：: SIAM J. Math. Anal. 48 (2016), no. 6, 4094--4125
DOI：: 10.1137/15M1049774

英文摘要：

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.

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