{"paper":{"title":"Stability estimates in $H^1_0$ for solutions of elliptic equations in varying domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gerassimos Barbatis, Jos\\'e M. Arrieta","submitted_at":"2012-05-09T16:32:13Z","abstract_excerpt":"We consider second-order uniformly elliptic operators subject to Dirichlet boundary conditions. Such operators are considered on a bounded domain $\\Omega$ and on the domain $\\phi(\\Omega)$ resulting from $\\Omega$ by means of a bi-Lipschitz map $\\phi$. We consider the solutions $u$ and $\\tilde u$ of the corresponding elliptic equations with the same right-hand side $f\\in L^2(\\Omega\\cup\\phi(\\Omega))$. Under certain assumptions we estimate the difference $\\|\\nabla\\tilde u-\\nabla u\\|_{L^2(\\Omega\\cup\\phi(\\Omega))}$ in terms of certain measure of vicinity of $\\phi$ to the identity map. For domains wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2027","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"}