{"paper":{"title":"Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"G. Barbatis, P.D. Lamberti, V.I. Burenkov","submitted_at":"2008-10-21T13:26:15Z","abstract_excerpt":"We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\\phi (\\Omega)$ parametrized by Lipschitz homeomorphisms $\\phi $ defined on a fixed reference domain $\\Omega$. Given two open sets $\\phi (\\Omega)$, $\\tilde \\phi (\\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\\|\\tilde \\phi -\\phi \\|_{W^{1,p}(\\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3823","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"}