{"paper":{"title":"Sub-criticality of non-local Schr\\\"odinger systems with antisymmetric potentials and applications to half-harmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Da Lio, Tristan Riviere","submitted_at":"2010-12-11T09:04:54Z","abstract_excerpt":"We consider nonlocal linear Schr\\\"odinger-type critical systems of the type\n  \\begin{equation}\\label{eqabstr}\n  \\Delta^{1/4} v=\\Omega\\, v~~~\\mbox{in $\\R\\,.$} \\\n  \\end{equation} where $\\Omega$ is antisymmetric potential in $L^2(\\R,so(m))$, $v$ is a ${\\R}^m$ valued map and $\\Omega\\, v$ denotes the matrix multiplication. We show that every solution $v\\in L^2(\\R,\\R^m)$ of \\rec{eqabstr} is in fact in $L^p_{loc}(\\R,\\R^m)$, for every $2\\le p<+\\infty$, in other words, we prove that the system (\\ref{eqabstr}) which is a-priori only critical in $L^2$ happens to have a subcritical behavior for antisymmet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2438","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"}