{"paper":{"title":"Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Luca Scarpa","submitted_at":"2016-11-21T14:05:43Z","abstract_excerpt":"We prove well-posedness for doubly nonlinear parabolic stochastic partial differential equations of the form $dX_t-\\text{div}\\,\\gamma(\\nabla X_t)\\,dt+\\beta(X_t)\\,dt\\ni B(t,X_t)\\,dW_t$, where $\\gamma$ and $\\beta$ are the two nonlinearities, assumed to be multivalued maximal monotone operators everywhere defined on $\\mathbb{R}^d$ and $\\mathbb{R}$ respectively, and $W$ is a cylindrical Wiener process. Using variational techniques, suitable uniform estimates (both pathwise and in expectation) and some compactness results, well-posedness is proved under the classical Leray-Lions conditions on $\\gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06790","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"}