Gamma-Compactness of a Class of Integrands with Nonstandard Coercivity and Growth Conditions

Abstract

We study the variational convergence of integral functionals F with integrands f(x, s, ξ) : Ω × ℝ × ℝd → ℝ, where f is a Carath´eodory 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.