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| $\Gamma$-CONVERGENCE OF INTEGRAL FUNCTIONALS DEPENDING ON VECTOR-VALUED FUNCTIONS OVER PARABOLIC DOMAINS |
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Citation： |
JIAN Huaiyu.$\Gamma$-CONVERGENCE OF INTEGRAL FUNCTIONALS DEPENDING ON VECTOR-VALUED FUNCTIONS OVER PARABOLIC DOMAINS[J].Chinese Annals of Mathematics B,2000,21(2):249~258 |
| Page view： 1046
Net amount： 776 |
Authors： |
JIAN Huaiyu; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No. 19701018). |
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| Abstract： |
This paper studies $\Gamma$-convergence for a sequence of parabolic
functionals,
$$F^\varepsilon (u)=\int_0^T\int_{\Omega} f(x/\varepsilon, t, \nabla u)
dxdt\ \text{as}\ \ \varepsilon \to 0,$$
where the integrand $f$ is nonconvex, and periodic on the first variable.
The author obtains the representation formula of the $\Gamma$-limit. The results
in this paper support a conclusion which relates $\Gamma$-convergence of
parabolic functionals to the associated gradient flows and confirms one of
De Giorgi's conjectures partially. |
Keywords： |
$\Gamma$-convergence, Parabolic-minima, Nonconvex functionals,
Parabolic |
Classification： |
35B27, 49J45 |
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