{"paper":{"title":"Caccioppoli--type estimates and Hardy--type inequalities derived from degenerated $p$--harmonic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnieszka Ka{\\l}amajska, Iwona Skrzypczak, Pavel Dr\\'abek","submitted_at":"2016-05-18T12:35:04Z","abstract_excerpt":"We obtain Caccioppoli--type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated $p$--Laplacian: $-\\Delta_{p,a} u:= -\\mathrm{div}(a(x)|\\na u|^{p-2}\\na u)\\ge b(x)\\Phi (u)$, where $u$ is defined in a domain $\\Omega$. Using Caccioppoli--type estimates, we obtain several variants of Hardy--type inequalities in weighted Sobolev spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05552","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"}