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Title: The Γ-convergence of oscillating integrands with nonstandard coercivity and growth conditions

We study the Γ-convergence as ε→0 of a family of integral functionals with integrand f{sub ε}(x,u,∇u), where the integrand oscillates with respect to the space variable x. The integrands satisfy a two-sided power estimate on the coercivity and growth with different exponents. As a consequence, at least two different variational Dirichlet problems can be connected with the same functional. This phenomenon is called Lavrent'ev's effect. We introduce two versions of Γ-convergence corresponding to variational problems of the first and second kind. We find the Γ-limit for the aforementioned family of functionals for problems of both kinds; these may be different. We prove that the Γ-convergence of functionals goes along with the convergence of the energies and minimizers of the variational problems. Bibliography: 23 titles. (paper)
Authors:
 [1] ;  [2]
  1. Vladimir State University (Russian Federation)
  2. Moscow State Technical University of Radio-Engineering, Electronics, and Automation (Russian Federation)
Publication Date:
OSTI Identifier:
22365290
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 4; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; DIRICHLET PROBLEM; FUNCTIONALS; INTEGRALS; MATHEMATICAL SOLUTIONS; SPACE; VARIATIONAL METHODS