{"paper":{"title":"The $\\Gamma$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Chambolle (CMAP), Giovanni Bellettini (DIPMAT), Michael Goldman (MPI-MIS)","submitted_at":"2013-01-22T12:35:21Z","abstract_excerpt":"In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functionals with discontinuities penalized with a \"cohesive\" energy, that is, whose cost depends on the actual opening of the discontinuity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5170","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"}