{"paper":{"title":"Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sekhar Ghosh, Souvik Bhowmick","submitted_at":"2024-10-06T10:40:24Z","abstract_excerpt":"In this paper, we prove the existence of weak, veryweak and duality solutions to a class of elliptic problems involving singularity and measure data which is given by: $-\\Delta u+(-\\Delta)^s u = \\frac{f(x)}{u^\\gamma} +\\mu$ in $\\Omega$ with the zero Dirichlet boundary data $u=0$ in $\\mathbb R^N \\setminus \\Omega$. The existence of weak solutions is obtained by approximating a sequence of problems for $0<\\gamma\\leq1$ and $\\gamma>1$. We employ Schauder's fixed point theorem and embeddings of Marcinkiewicz spaces. The novelty of our work is that we prove the existence of a duality solution and its "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.04441","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.04441/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}