{"paper":{"title":"Nonconvex minimization related to quadratic double-well energy - approximation by convex problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Computer Science, Cz\\k{e}stochowa, Faculty of Mathematics, Faculty of Mechanical Engineering, Institute of Mathematics, Natural Sciences. College of Sciences, Poland), Poland) Piotr Pucha{\\l}a (Technical University of Cz\\k{e}stochowa, Warsaw, Zdzis{\\l}aw Naniewicz (Cardinal Stefan Wyszy\\'nski University","submitted_at":"2009-07-06T22:49:19Z","abstract_excerpt":"A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied with taking into account the minimization of the corresponding integral functional. Such integral, as being not sequentially weakly lower semicontinuous, does not admit classical minimizers. To derive the relaxation formula for the infimum, the minimizing sequence consisting of solutions of convex problems appropriately approximating the original nonconvex one is constructed. The weak limit of this sequence together with the weak limit of the sequence of solutions of the corresponding dual"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1120","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"}