GAMMA-COMPACTNESS OF A CLASS OF INTEGRANDS WITH NONSTANDARD COERCIVITY AND GROWTH CONDITIONS

摘要

We study the variational convergence of integral functionals F with integrands f(x, s, ξ) : Ω × R × R~d → R, where f is a Caratheodory function continuous with respect to s and ξ, convex with respect to ξ, and satisfying a two-sided power estimate of coercivity and growth with exponents α and β, d ＜ α ≤β ＜ ∞. For α ＜ β with the functional F we associate variational Dirichlet problems of the first and second type. For the class of such integrands we prove the compactness principle relative to -convergence of two types. Bibliography: 6 titles.