A characterization of relatively compact sets in L^p(Ω,B): Dedicated to Professor Gheorghe Coman on the occasion of his 80th anniversary - GAHN, Markus; NEUSS-RADU, Maria (Studia Universitatis Babeș-Bolyai Mathematica, 2016)
We give a characterization of relatively compact sets F in L^p(Ω,B) for p[1,∞), B a Banach-space, and Ω ^n. This is a generalization of the results obtained in Simon for the space L^p((0,T),B) with T>0, first to rectangles Ω =(a,b) ^n and, under additional conditions, to arbitrary open and bounded subsets of ^n. An application of the main compactness result to a problem arising in homogenization of processes on periodic surfaces is given. Mathematics Subject Classification (2010): 35K57, 46E40, 46B50.