{"paper":{"title":"Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Medea Tsaava, Roland Duduchava","submitted_at":"2016-05-29T16:59:54Z","abstract_excerpt":"The purpose of the present research is to investigate model mixed boundary value problems for the Helmholtz equation in a planar angular domain $\\Omega_\\alpha\\subset\\mathbb{R}^2$ of magnitude $\\alpha$. The BVP is considered in a non-classical setting when a solution is sought in the Bessel potential spaces $\\mathbb{H}^s_p(\\Omega_\\alpha)$, $s>1/p$, $1<p<\\infty$. The problems are investigated using the potential method by reducing them to an equivalent boun\\-dary integral equation (BIE) in the Sobolev-Slobode\\v{c}kii space on a semi-infinite axes $\\bW^{s-1/p}_p(\\bR^+)$, which is of Mellin convol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09029","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"}