{"paper":{"title":"A general class of free boundary problems for fully nonlinear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Henrik Shahgholian","submitted_at":"2013-09-03T19:22:38Z","abstract_excerpt":"In this paper we consider the fully nonlinear parabolic free boundary problem $$ \\left\\{\\begin{array}{ll} F(D^2u) -\\partial_t u=1 & \\text{a.e. in}Q_1 \\cap \\Omega\\\\ |D^2 u| + |\\partial_t u| \\leq K & \\text{a.e. in}Q_1\\setminus\\Omega, \\end{array} \\right. $$ where $K>0$ is a positive constant, and $\\Omega$ is an (unknown) open set.\n  Our main result is the optimal regularity for solutions to this problem: namely, we prove that $W_x^{2,n} \\cap W_t^{1,n} $ solutions are locally $C_x^{1,1}\\cap C_t^{0,1} $ inside $Q_1$. A key starting point for this result is a new BMO-type estimate which extends to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0782","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"}