{"paper":{"title":"The $p$-CurlCurl : Spaces, traces, coercivity and a Helmholtz decomposition in $L^p$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marc Laforest","submitted_at":"2018-08-17T19:54:44Z","abstract_excerpt":"This work provides the foundation for the finite element analysis of an elliptic problem which is the rotational analogue of the $p$-Laplacian and which appears as a model of the magnetic induction in a high-temperature superconductor operating near it's critical current. Whereas the function theory for the $p$-Laplacian requires standard results in $L^p$ Sobolev spaces, this problem requires an extension to $L^p$ spaces of the well-known $L^2$ theory for divergence free vector fields, as used in the finite element method applied to incompressible flows and electromagnetic radiation. Among oth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05976","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"}