{"paper":{"title":"Variational methods for the selection of solutions to an implicit system of PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Giovanni Pisante, Gisella Croce","submitted_at":"2016-09-09T11:13:29Z","abstract_excerpt":"We consider the vectorial system \\[ \\begin{cases} Du \\in \\mathcal{O}(2), & \\mbox{a.e. in}\\;\\Omega, u=0, & \\mbox{on} \\;\\partial \\Omega, \\end{cases} \\] where $\\Omega$ is a subset of $\\R^2$, $u:\\Omega\\to \\R^2$ and $\\mathcal{O}(2)$ is the orthogonal group of $\\R^2$. We provide a variational method to select, among the infinitely many solutions, the ones that minimize an appropriate weighted measure of the singular set of the gradient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02743","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"}