{"paper":{"title":"Convergence of invariant measures for singular stochastic diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Ioana Ciotir, Jonas M. T\\\"olle","submitted_at":"2012-01-13T13:49:25Z","abstract_excerpt":"It is proved that the solutions to the singular stochastic $p$-Laplace equation, $p\\in (1,2)$ and the solutions to the stochastic fast diffusion equation with nonlinearity parameter $r\\in (0,1)$ on a bounded open domain $\\Lambda\\subset\\R^d$ with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters $p$ and $r$ respectively (in the Hilbert spaces $L^2(\\Lambda)$, $H^{-1}(\\Lambda)$ respectively). The highly singular limit case $p=1$ is treated with the help of stochastic evolution variational inequalities, where $\\mathbbm{P}$-a.s. convergence, uni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2839","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}