{"paper":{"title":"Inverse iteration for $p$-ground states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erik Lindgren, Ryan Hynd","submitted_at":"2015-02-10T10:16:47Z","abstract_excerpt":"We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for $p\\in (1,\\infty)$ and a given domain $\\Omega\\subset\\mathbb{R}^n$, we analyze a scheme that allows us to approximate the smallest value the ratio $\\int_\\Omega|D\\psi|^p dx/\\int_\\Omega|\\psi|^p dx$ can assume for functions $\\psi$ that vanish on $\\partial \\Omega$. The scheme in question also provides a natural way to approximate minimizing $\\psi$. Our analysis also extends in the limit as $p\\rightarrow\\infty$ and thereby fashions a new approximation method for ground states of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02837","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"}