The Γ-convergence of oscillating integrands with nonstandard coercivity and growth conditions
- Vladimir State University (Russian Federation)
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)
- OSTI ID:
- 22365290
- Journal Information:
- Sbornik. Mathematics, Vol. 205, Issue 4; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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