{"paper":{"title":"Kato's inequality when $\\Delta u$ is a measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Augusto C. Ponce, Ha\\\"im Brezis","submitted_at":"2013-12-23T09:48:50Z","abstract_excerpt":"We extend the classical Kato's inequality in order to allow functions $u \\in L^1_\\mathrm{loc}$ such that $\\Delta u$ is a Radon measure. This inequality has been applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation $- \\Delta u + g(u) = \\mu$, where $\\mu$ is a measure and $g : \\mathbb{R} \\to \\mathbb{R}$ is an increasing continuous function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6498","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"}