Rellich selection theorem

Let D be an open subset of n. If, for a sequence of functions fi:D, i=1,2, there exists a constant B>0 such that

(i)  fiL2(D)=Dfi2dnx<B


(i)(j{1,n})  D(fixj)2dnx<B

then there exists a subsequence which is convergent in the L2(D) norm.

Title Rellich selection theorem
Canonical name RellichSelectionTheorem
Date of creation 2013-03-22 14:38:55
Last modified on 2013-03-22 14:38:55
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 7
Author rspuzio (6075)
Entry type Theorem
Classification msc 46C05