{"paper":{"title":"Evolution equations on non flat waveguides","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Piero D'Ancona, Reinhard Racke","submitted_at":"2010-10-05T09:38:09Z","abstract_excerpt":"We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator $H=-\\Delta_{x}-\\Delta_{y}+V(x,y)$ with Dirichled boundary condition on an unbounded domain $\\Omega$, and we introduce the notion of a \\emph{repulsive waveguide} along the direction of the first group of variables $x$. If $\\Omega$ is a repulsive waveguide, we prove a sharp estimate for the Helmholtz equation $Hu-\\lambda u=f$. As consequences we prove smoothing estimates for the Schr\\\"odinger and wave equations associated to $H$, and Strichartz estimates for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0817","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"}