{"paper":{"title":"Nonlocal problem for Laplace equation in Bochner spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Bilal Bilalov, Lubomira Softova, Pia Salerno, Sabina Sadigova","submitted_at":"2026-05-25T12:15:02Z","abstract_excerpt":"We study the Laplace equation posed in the unbounded rectangular domain $\\Pi = I \\times (0,\\infty)$ with $I= (0,2\\pi)$, and subject to nonlocal boundary conditions on $\\partial \\Pi$ in the trace sense. The analysis is carried out in the Bochner-Sobolev space $W^2_{p,1}(\\Pi;X)$, associated with the Bochner space $L^{p,1}(\\Pi;X)$, with $ p \\in (1,\\infty)$ and $X$ is a suitable Banach space. To solve the problem, we employ a generalized spectral method. In particular, we introduce the notion of $\\otimes$-basis generated by tensor products and extend the classical scheme known from the scalar case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25761","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25761/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}