{"paper":{"title":"On the Dirichlet problem in cylindrical domains for evolution Ole\\v{\\i}nik--Radkevi\\v{c} PDE's: a Tikhonov-type theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessia E. Kogoj","submitted_at":"2019-03-20T12:13:07Z","abstract_excerpt":"We consider the linear second order PDO's $$ \\mathscr{L} = \\mathscr{L}_0 - \\partial_t : = \\sum_{i,j =1}^N \\partial_{x_i}(a_{i,j} \\partial_{x_j} ) - \\sum_{j=i}^N b_j \\partial_{x_j} - \\partial _t,$$and assume that $\\mathscr{L}_0$ has nonnegative characteristic form and satisfies the Ole\\v{\\i}nik--Radkevi\\v{c} rank hypoellipticity condition. These hypotheses allow the construction of Perron-Wiener solutions of the Dirichlet problems for $\\mathscr{L}$ and $\\mathscr{L}_0$ on bounded open subsets of $\\mathbb R^{N+1}$ and of $\\mathbb R^{N}$, respectively.\n  Our main result is the following Tikhonov-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08463","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"}