{"paper":{"title":"Existence results of two mixed boundary value elliptic PDEs in $\\mathbb{R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Akasmika Panda, Debajyoti Choudhuri","submitted_at":"2019-05-01T09:34:53Z","abstract_excerpt":"We study the existence of a solution to the mixed boundary value problem for Helmholtz and Poisson type equations in a bounded Lipschitz domain $\\Omega\\subset\\mathbb{R}^N$ and in $\\mathbb{R}^N\\setminus\\Omega$ for $N\\geq3$. The boundary $\\partial\\Omega$ of $\\Omega$ is the decomposition of $\\Gamma_1,\\Gamma_2\\subset\\partial\\Omega$ such that $\\partial\\Omega=\\Gamma=\\overline{\\Gamma}_1\\cup\\Gamma_2=\\Gamma_1\\cup\\overline{\\Gamma}_2$ and $\\Gamma_1\\cap\\Gamma_2=\\emptyset$. We have shown that if the Neumann data $f_2\\in H^{-\\frac{1}{2}}(\\Gamma_2)$ and the Dirichlet data $f_1\\in H^{\\frac{1}{2}}(\\Gamma_1)$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00232","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"}