{"paper":{"title":"A Description of All Self-Adjoint Extensions of the Laplacian and Krein-Type Resolvent Formulas on Nonsmooth Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Fritz Gesztesy, Marius Mitrea","submitted_at":"2009-07-10T16:56:42Z","abstract_excerpt":"This paper has two main goals. First, we are concerned with the classification of self-adjoint extensions of the Laplacian $-\\Delta\\big|_{C^\\infty_0(\\Omega)}$ in $L^2(\\Omega; d^n x)$. Here, the domain $\\Omega$ belongs to a subclass of bounded Lipschitz domains (which we term quasi-convex domains), which contain all convex domains, as well as all domains of class $C^{1,r}$, for $r\\in(1/2,1)$. Second, we establish Krein-type formulas for the resolvents of the various self-adjoint extensions of the Laplacian in quasi-convex domains and study the properties of the corresponding Weyl--Titchmarsh op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1750","kind":"arxiv","version":4},"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"}