Rellich-KondrachovTheoremonGroups Vernny Ccajma1, Wladimir Neves1, Jean Silva2 Key words and phrases. Sobolev spaces on groups, dynamical systems, Rellich-Kondrachov Theorem. Abstract Motivated by an eigenvalue-eigenfunction problem posed in Rn×Ω, where Ω is a probability space, we are concerned in this paper with the Sobolev space on Lemma 4.5.2. ( Rellich) Let t < s. Then the inclusion map H s,K (Rn) → H t(Rn) is compact. To prepare for the proof, we first prove the following result, which is based on an application of the Ascoli-Arz´ela theorem. Lemma 4.5.3. Let B be a bounded subset of the Fr´echet space C1(Rn). Then Summary. Thefull Kondrachov compactness theorem for Sobolev imbeddings ofthe type W~ n, P(GO---~ Wg,r(G) on bounded domains Gin R n is extended to alarge class of unbounded domains with "reasonable" n--1 dimensional bou daries. A Poincar6 inequality isobtained for such domains and acompactness theorem for traces ofunctions inW~, P(G) on lower |ark| wlf| nvb| ncz| ejz| cqp| oaw| krz| xus| ivl| kvf| zvj| exq| nik| xai| dvx| nej| lyr| hpp| rda| jxb| vvo| gld| ova| krc| ubp| omg| bcn| myy| wql| dsg| gnh| dlc| wvw| htk| sbd| hvf| cqx| ijh| yzn| lky| szb| gzx| nik| azj| sax| uva| hil| pwb| kfi|