{"paper":{"title":"A right inverse operator for $\\operatorname{curl}+\\lambda$ and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Briceyda B. Delgado, Vladislav V. Kravchenko","submitted_at":"2018-12-18T13:48:20Z","abstract_excerpt":"A general solution of the equation $\\operatorname{curl}\\vec{w}+\\lambda\\vec {w}=\\overrightarrow{g},\\,\\lambda\\in\\mathbb{C},\\,\\lambda\\neq0$ is obtained for an arbitrary bounded domain $\\Omega\\subset\\mathbb{R}^{3}$ with a Liapunov boundary and $\\overrightarrow{g}\\in W^{p,\\operatorname{div}}\\left( \\Omega\\right) =\\left\\{ \\overrightarrow{u}\\in L^{p}\\left( \\Omega\\right) :\\,\\operatorname{div}\\overrightarrow{u}\\in L^{p}\\left( \\Omega\\right) ,\\,1<p<\\infty\\right\\} $. The result is based on the use of classical integral operators of quaternionic analysis.\n  Applications of the main result are considered to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07364","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"}