{"paper":{"title":"Density estimates for Ginzburg-Landau energies with degenerate double-well potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chilin Zhang, Ovidiu Savin","submitted_at":"2025-06-20T13:51:55Z","abstract_excerpt":"We consider a class of Allen-Cahn equations associated with Ginzburg-Landau energies involving degenerate double-well potentials that vanish of order $m$ at the minima \\begin{equation}\n  J(v,\\Omega)=\\int_{\\Omega}\\Big\\{|\\nabla v|^{p}+(1-v^{2})^{m}\\Big\\}dx,\\quad 1<p<m, \\end{equation} and establish density estimates for the level sets of nontrivial minimizers $|v| \\leq 1$. This extends a result of Dipierro-Farina-Valdinoci where the density estimates for such degenerate potentials were obtained for a bounded range of $m$'s. The original estimates for the classical case $p=m=2$ were established by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17000","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.17000/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}