{"paper":{"title":"On local non-zero constraints in PDE with analytic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni S. Alberti, Yves Capdeboscq","submitted_at":"2015-01-07T11:25:36Z","abstract_excerpt":"We consider the Helmholtz equation with real analytic coefficients on a bounded domain $\\Omega\\subset\\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\\omega$ in a fixed interval $[a,b]$. We consider a constraint on the solutions $u_{\\omega}^{i}$ of the form $\\zeta(u_{\\omega}^{1},\\ldots,u_{\\omega}^{d+1},\\nabla u_{\\omega}^{1},\\ldots,\\nabla u_{\\omega}^{d+1})\\neq0$, where $\\zeta$ is analytic, which is satisfied in $\\Omega$ when $\\omega=0$. We show that for any $\\Omega^{\\prime}\\Subset\\Omega$ and almost any $d+1$ frequencies $\\omega_{k}$ in $[a,b]$, there exist "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01449","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"}