{"paper":{"title":"Regularity for multi-phase variational problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cristiana De Filippis, Jehan Oh","submitted_at":"2018-07-08T20:35:30Z","abstract_excerpt":"We prove $C^{1,\\nu}$ regularity for local minimizers of the \\oh{multi-phase} energy: \\begin{flalign*} w \\mapsto \\int_{\\Omega}\\snr{Dw}^{p}+a(x)\\snr{Dw}^{q}+b(x)\\snr{Dw}^{s} \\ dx, \\end{flalign*} under sharp assumptions relating the couples $(p,q)$ and $(p,s)$ to the H\\\"older exponents of the modulating coefficients $a(\\cdot)$ and $b(\\cdot)$, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02880","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"}