{"paper":{"title":"Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.AP"],"primary_cat":"math.OC","authors_text":"Piermarco Cannarsa (DIPMAT), Pierre Cardaliaguet (CEREMADE)","submitted_at":"2011-03-23T06:17:31Z","abstract_excerpt":"Solutions of the Hamilton-Jacobi equation $H(x,-Du(x))=1$, with $H(\\cdot,p)$ H\\\"older continuous and $H(x,\\cdot)$ convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the ${\\mathcal C}^{1,\\alpha}$-regularity of the extremal trajectories associated with the multifunction generated by $D_pH$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4454","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"}