{"paper":{"title":"Null quadrature domains and a free boundary problem for the Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Avmir S. Margulis, Lavi Karp","submitted_at":"2010-03-04T14:10:42Z","abstract_excerpt":"Null quadrature domains are unbounded domains in $\\R^n$ ($n \\geq 2$) with external gravitational force zero in some generalized sense. In this paper we prove that the complement of null quadrature domain is a convex set with real analytic boundary. We establish the quadratic growth estimate for the Schwarz potential of a null quadrature domain which reduces our main result to Theorem II of the paper of Caffarelli, Karp and Shahgholian (Ann. Math. 151(2000), 269-292), on the regularity of solution to the classical global free boundary problem for Laplacian. We also show that any null quadrature"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1054","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"}