{"paper":{"title":"Energy estimates and cavity interaction for a critical-exponent cavitation model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Duvan Henao, Sylvia Serfaty","submitted_at":"2011-08-03T20:06:17Z","abstract_excerpt":"We consider the minimization of $\\int_{\\Omega_{\\ep}} |D\\vec u|^p \\dd\\vec x$ in a perforated domain $\\Omega_{\\ep}:= \\Omega \\setminus \\bigcup_{i=1}^M B_{\\ep}(\\vec a_i)$ of $\\R^n$, among maps $\\vec u \\in W^{1,p}(\\Omega_{\\ep}, \\R^n)$ that are incompressible ($\\det D\\vec u\\equiv 1$), invertible, and satisfy a Dirichlet boundary condition $\\vec u= \\vec g$ on $\\partial \\Omega$. If the volume enclosed by $\\vec g (\\partial \\Omega)$ is greater than $|\\Omega|$, any such deformation $\\vec u$ is forced to map the small holes $B_{\\ep}(\\vec a_i)$ onto macroscopically visible cavities (which do not disappear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0939","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"}