{"paper":{"title":"An $L^{p}$--approach to the well-posedness of transport equations associated to a regular field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bertrand Lods, Luisa Arlotti","submitted_at":"2018-06-11T14:14:10Z","abstract_excerpt":"We investigate transport equations associated to a Lipschitz field  on some subspace of $\\mathbb{R}^N$ endowedwith a general  measure $\\mu$ in  $L^{p}$-spaces $1 < p <\\infty$, extending the results obtained in two previous contributions of the author in the $L^{1}$-context.  We notably prove the well-posedness of  boundary-value transport problems with a large variety of boundary conditions. New explicit formula for the transport semigroup are in particular given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04006","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"}