{"paper":{"title":"A nonlinear free boundary problem with a self-driven Bernoulli condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram Karakhanyan, Enrico Valdinoci, Serena Dipierro","submitted_at":"2016-11-01T22:41:17Z","abstract_excerpt":"We study a Bernoulli type free boundary problem with two phases $$J[u]=\\int_{\\Omega}|\\nabla u(x)|^2\\,dx+\\Phi\\big({\\mathcal M}_-(u), {\\mathcal{M}}_+(u)\\big), \\quad u-\\bar u\\in W^{1,2}_0(\\Omega), $$ where $\\bar u\\in W^{1,2}(\\Omega)$ is a given boundary datum. Here, ${\\mathcal M}_1$ and ${\\mathcal M}_2$ are weighted volumes of $\\{u\\le 0\\}\\cap \\Omega$ and $\\{u>0\\}\\cap \\Omega$, respectively, and $\\Phi$ is a nonnegative function of two real variables.\n  We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00412","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"}