{"paper":{"title":"Lipschitz regularity for local minimizers of some widely degenerate problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Lorenzo Brasco, Pierre Bousquet, Vesa Julin","submitted_at":"2014-09-07T20:48:32Z","abstract_excerpt":"We consider local minimizers of the functional \\[ \\sum_{i=1}^N \\int (|u_{x_i}|-\\delta_i)^p_+\\, dx+\\int f\\, u\\, dx, \\] where $\\delta_1,\\dots,\\delta_N\\ge 0$ and $(\\,\\cdot\\,)_+$ stands for the positive part. Under suitable assumptions on $f$, we prove that local minimizers are Lipschitz continuous functions if $N=2$ and $p\\ge 2$, or if $N\\ge 2$ and $p\\ge 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2162","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"}