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The critical points of this functional satisfy a possibly singular or degenerate, quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential $F(u)$ and we deduce several rigidity and symmetry properties."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.2303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-10T10:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"6b7d7d96f2c877389704c8c39c413d6c747ae9bc1a25a76198e8baf35da2126e","abstract_canon_sha256":"8391efad30199059771226b66399df3eb9861270b92515b445ac59e1b15f30a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:47.750944Z","signature_b64":"dPqzgfg4BO8bPChNJGYgQpKehu2AOpNEwCuIkUZ3ejiDP5UbJibp62RU/W5NJGIn9vfVRXd/+keTQF4Po1WUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"440f3606accfabced34a83a52792cb463813b11e4b1c8e853a5afadd78a765c9","last_reissued_at":"2026-05-18T02:30:47.750416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:47.750416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Farina, Enrico Valdinoci, Matteo Cozzi","submitted_at":"2013-05-10T10:42:24Z","abstract_excerpt":"We consider the Wulff-type energy functional $$ \\mathcal{W}_\\Omega(u) := \\int_\\Omega B(H(\\nabla u (x))) - F(u(x)) \\, dx, $$ where $B$ is positive, monotone and convex, and $H$ is positive homogeneous of degree 1. 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