{"paper":{"title":"Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fritz Gesztesy, Roger Nichols, Steve Hofmann","submitted_at":"2014-11-18T09:59:51Z","abstract_excerpt":"We discuss stability of square root domains for uniformly elliptic partial differential operators $L_{a,\\Omega,\\Gamma} = -\\nabla\\cdot a \\nabla$ in $L^2(\\Omega)$, with mixed boundary conditions on $\\partial \\Omega$, with respect to additive perturbations. We consider open, bounded, and connected sets $\\Omega \\in \\mathbb{R}^n$, $n \\in \\mathbb{N} \\backslash\\{1\\}$, that satisfy the interior corkscrew condition and prove stability of square root domains of the operator $L_{a,\\Omega,\\Gamma}$ with respect to additive potential perturbations $V \\in L^p(\\Omega) + L^{\\infty}(\\Omega)$, $p>n/2$.\n  Special"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4789","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"}