Anna S. Khripunova Balci: Variational convergence of integrands with non-standart growth conditions

We study the variational convergence of integral functionals F with integrands f(x, s, ξ) : Ω × ℝ × ℝ^d → ℝ, where f is a Carathéodory 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 Γ-convergence of two types.