{"paper":{"title":"BV functions in a Gelfand triple for differentiable measure and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Michael R\\\"ockner, Rongchan Zhu, Xiangchan Zhu","submitted_at":"2012-09-13T18:08:09Z","abstract_excerpt":"In this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [RZZ12], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $\\Gamma$ in a Banach space $E$. We prove the existence of a martingale solution of this problem if $\\Gamma$ is a regular convex set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2980","kind":"arxiv","version":2},"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"}