On Integral Representation of Γ-Limit Functionals
- 作者: Zhikov V.1, Pastukhova S.2
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隶属关系:
- Vladimir State University
- Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
- 期: 卷 217, 编号 6 (2016)
- 页面: 736-750
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238138
- DOI: https://doi.org/10.1007/s10958-016-3002-z
- ID: 238138
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详细
We consider the Γ-convergence of a sequence of integral functionals Fn(u), defined on the functions u from the Sobolev space W1,α(Ω) (α > 1); Ω is a bounded Lipschitz domain, where the integrand fn(x, u,∇u) depends on a function u and its gradient ∇u. As functions of ξ, the integrands fn(x, s, ξ) are convex and satisfy a two-sided power estimate on the coercivity and growth with different exponents α < β. Moreover, the integrands fn(x, s, ξ) are equi-continuous over s in some sense with respect to n. We prove that for the functions from L ∞ (Ω) ∩ W1,β(Ω) the Γ-limit functional coincides with an integral functional F(u) for which the integrand f(x, s, ξ) is of the same class as fn(x, s, ξ).
作者简介
V. Zhikov
Vladimir State University
编辑信件的主要联系方式.
Email: zhikov@vlsu.ru
俄罗斯联邦, Vladimir
S. Pastukhova
Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Email: zhikov@vlsu.ru
俄罗斯联邦, Moscow