{"paper":{"title":"Optimal observability of the multi-dimensional wave and Schr\\\"odinger equations in quantum ergodic domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.OC","authors_text":"Emmanuel Tr\\'elat, Enrique Zuazua, Yannick Privat","submitted_at":"2012-11-24T10:04:07Z","abstract_excerpt":"We consider the wave and Schr\\\"odinger equations on a bounded open connected subset $\\Omega$ of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset $\\omega$ of $\\Omega$ during a time interval [0,T] with T>0. We address the problem of the optimal location of the observation subset \\omega among all possible subsets of a given measure or volume fraction. We solve it in two different situations. First, when a specific choice of the initial data is given and therefore we dea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5655","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"}