Università degli Studi di Trento, Dipartimento di Matematica, via Sommarive 14, 38050 Povo (Trento), Italia; Visintin@science.unitn.it
We define and characterize weak and strong two-scale convergence in Lp , C 0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive two-scale versions of the classic theorems of Rellich, Sobolev, and Morrey.
(Received September 9 2004)
(Revised April 5 2005)
(Online publication June 20 2006)
Mathematics Subject Classification: