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

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en Gess, Benjamin Tölle, Jonas 2018-11-09T13:07:41Z 2018-11-09T13:07:41Z 2016-12-08
dc.identifier.citation Gess , B & Tölle , J 2016 , ' Ergodicity and local limits for stochastic local and nonlocal p -Laplace equations ' SIAM JOURNAL ON MATHEMATICAL ANALYSIS , vol 48 , no. 6 , pp. 4094-4125 . DOI: 10.1137/15M1049774 en
dc.identifier.issn 0036-1410
dc.identifier.issn 1095-7154
dc.identifier.other PURE UUID: b45eed30-6bf9-42bf-8d9f-57094e9448c7
dc.identifier.other PURE ITEMURL:
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dc.description.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 [B. Gess and J. M. Tölle, J. Math. Pures Appl., 101 (2014), pp. 789--827], [W. Liu and J. M. Tölle, Electron. Commun. Probab., 16 (2011), pp. 447--457], [W. Liu, J. Evol. Equations, 9 (2009), pp. 747--770]. In particular, the results include the multivalued case of the stochastic (nonlocal) total variation flow, which solves an open problem raised in [V. Barbu, G. Da Prato, and M. Röckner, SIAM J. Math. Anal., 41 (2009), pp. 1106--1120]. 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. en
dc.format.extent 4094-4125
dc.format.mimetype application/pdf
dc.language.iso en en
dc.relation.ispartofseries SIAM JOURNAL ON MATHEMATICAL ANALYSIS en
dc.relation.ispartofseries Volume 48, issue 6 en
dc.rights openAccess en
dc.subject.other 111 Mathematics en
dc.title Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department Max-Planck-Institute for Mathematics in the Sciences
dc.contributor.department Department of Mathematics and Systems Analysis
dc.subject.keyword Stochastic variational inequality
dc.subject.keyword Nonlocal stochastic partial differential equations
dc.subject.keyword Singular-degenerate SPDE
dc.subject.keyword stochastic $p$-Laplace equation
dc.subject.keyword ergodicity
dc.subject.keyword 111 Mathematics
dc.identifier.urn URN:NBN:fi:aalto-201811095681
dc.identifier.doi 10.1137/15M1049774
dc.type.version publishedVersion

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