{"paper":{"title":"Existence and Uniqueness of Global Strong Solutions to Fully Nonlinear Second Order Elliptic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis (Reading, UK)","submitted_at":"2014-08-22T20:53:03Z","abstract_excerpt":"We consider the problem of existence and uniqueness of strong a.e. solutions $u: \\mathbb{R}^n \\longrightarrow \\mathbb{R}^N$ to the fully nonlinear PDE system \\[\\label{1} \\tag{1} F(\\cdot,D^2u ) \\,=\\, f, \\ \\ \\text{ a.e. on }\\mathbb{R}^n, \\] when $ f\\in L^2(\\mathbb{R}^n)^N$ and $F$ is a Carath\\'eodory map. \\eqref{1} has not been considered before. The case of bounded domains has been studied by several authors, firstly by Campanato and under Campanato's ellipticity condition on $F$. By introducing a new much weaker notion of ellipticity, we prove solvability of \\eqref{1} in a tailored Sobolev \"en"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5423","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"}