{"paper":{"title":"The p-Laplace equation in domains with multiple crack section via pencil operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pablo Alvarez-Caudevilla, Victor A. Galaktionov","submitted_at":"2013-10-02T10:48:58Z","abstract_excerpt":"The p-Laplace equation\n  $$ \\n \\cdot (|\\n u|^n \\n u)=0 \\whereA n>0, $$ in a bounded domain $\\O \\subset \\re^2$, with inhomogeneous Dirichlet conditions on the smooth boundary $\\p \\O$ is considered. In addition, there is a finite collection of curves\n  $$\\Gamma = \\Gamma_1\\cup...\\cup\\Gamma_m \\subset \\O, \\quad \\{on which we assume homogeneous Dirichlet boundary conditions} \\quad u=0, $$ modeling a multiple crack formation, focusing at the origin $0 \\in \\O$. This makes the above quasilinear elliptic problem overdetermined. Possible types of the behaviour of solution $u(x,y)$ at the tip 0 of such ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0812","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"}