Homogenization of besicovitch type almost periodic functionals

Abstract

It is considered a function and w in the Muckenhoupt class A _P , such that for every is almost periodic in the sense of Besicovitch and for every is convex. Then it is introduced a convex function , explicitly deduced f by such that for every bounded open set ω with Lipschitz boundary ψ and in L ^∞(ω) the solutions of the problems min converge, up to subsequences, in L ¹(ω) to solutions of min and the convergence of the whole sequence of the minimum values holds.

Keywords:

• Calculus of variations
• degenerate problems
• homogenization
• almost periodicity
• Muckenhoupt classes

AMS(MOS)::

• 35J70
• 49A21