Calculus of Variations, Homogenization and Continuum Mechanics
1994
Let F (u) = ∫ 1 0 f(u, u) dt be a weakly lower semicontinuous autonomous functional defined for all functions u : [0, 1] → R in the Sobolev space W . We show that under suitable hypotheses F agrees with the relaxation of the same functional restricted to regular functions, i.e., that for every function u there exist regular functions uh such that uh → u in the W 1,p norm and F (uh) → F (u). 1991 AMS Subject Classification: 49J45