On Integral Representation of Γ-Limit Functionals
- Авторлар: Zhikov V.1, Pastukhova S.2
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Мекемелер:
- Vladimir State University
- Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
- Шығарылым: Том 217, № 6 (2016)
- Беттер: 736-750
- Бөлім: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/238138
- DOI: https://doi.org/10.1007/s10958-016-3002-z
- ID: 238138
Дәйексөз келтіру
Аннотация
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).
Авторлар туралы
V. Zhikov
Vladimir State University
Хат алмасуға жауапты Автор.
Email: zhikov@vlsu.ru
Ресей, Vladimir
S. Pastukhova
Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
Email: zhikov@vlsu.ru
Ресей, Moscow