{"paper":{"title":"Nonhomogeneous Boundary Value Problems of Nonlinear Schr\\\"odinger Equations in a Half Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bing-Yu Zhang, Shu-Ming Sun, Yu Ran","submitted_at":"2016-09-18T03:37:51Z","abstract_excerpt":"This paper discusses the initial-boundary-value problems (IBVP) of nonlinear Schr\\\"odinger equations posed in a half plane $\\mathbb{R} \\times \\mathbb{R}^+$ with nonhomogeneous Dirichlet boundary conditions. For any given $s \\ge 0$, if the initial data $\\varphi (x, y)$ are in Sobolev space $H^s(\\mathbb{R}\\times \\mathbb{R}^+) $ with the boundary data $ h ( x, t) $ in an optimal space ${\\cal H}^s(0,T)$ as defined in the introduction, which is slightly weaker than the space $$H^{(2s+1)/4}_{t} ([0, T]; L_x^2(\\mathbb{R} ) ) \\cap L^2_t ( [ 0, T]; H^{s+ 1/2} _x ( \\mathbb{R} ) ),$$ the local well-posed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05418","kind":"arxiv","version":2},"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"}