{"paper":{"title":"Approximation of Relaxed Dirichlet Problems by Boundary Value problems in perforated domains","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"funct-an","authors_text":"Annalisa Malusa, Gianni Dal Maso","submitted_at":"1993-03-26T11:23:54Z","abstract_excerpt":"Given an elliptic operator~$L$ on a bounded domain~$\\Omega \\subseteq {\\bf R}^n$, and a positive Radon measure~$\\mu$ on~$\\Omega$, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of domains~$\\Omega_h \\subseteq \\Omega$ with the following property: for every~$f\\in H^{-1}(\\Omega)$ the sequence~$u_h$ of the solutions of the Dirichlet problems~$L\\, u_h=f$ in~$\\Omega_h$, $u_h=0$ on~$\\partial \\Omega_h$, extended to 0 in~$\\Omega \\setminus \\Omega_h$, converges to the solution of the \\lq\\lq relaxed Dirichlet problem\\rq\\rq\\ $L\\,u+\\mu u=f$ in~$\\Omega$, $u=0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9303004","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"}