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| Homogenization of Elliptic Problems with Quadratic Growth and Nonhomogenous Robin Conditions in Perforated Domains |
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Citation： |
Imen CHOURABI,Patrizia DONATO.Homogenization of Elliptic Problems with Quadratic Growth and Nonhomogenous Robin Conditions in Perforated Domains[J].Chinese Annals of Mathematics B,2016,37(6):833~852 |
| Page view： 1789
Net amount： 1384 |
Authors： |
Imen CHOURABI; Patrizia DONATO |
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| Abstract： |
This paper deals with the homogenization of a class of nonlinear
elliptic problems with quadratic growth in a periodically perforated
domain. The authors prescribe a Dirichlet condition on the exterior
boundary and a nonhomogeneous nonlinear Robin condition on the
boundary of the holes. The main difficulty, when passing to the
limit, is that the solution of the problems converges neither
strongly in $L^2(\Omega)$ nor almost everywhere in $\Omega$. A new
convergence result involving nonlinear functions provides suitable
weak convergence results which permit passing to the limit without
using any extension operator. Consequently, using a corrector result
proved in [Chourabi, I. and Donato, P., Homogenization and
correctors of a class of elliptic problems in perforated domains,
{\it Asymptotic Analysis}, {\bf 92}(1), 2015, 1--43, DOI:
10.3233/ASY-151288], the authors describe the limit problem,
presenting a limit nonlinearity which is different for the two
cases, that of a Neumann datum with a nonzero average and with a
zero average. |
Keywords： |
Homogenization, Elliptic problems, Quadratic growth,
Nonhomogeneous Robin boundary conditions, Perforated domains |
Classification： |
17B40, 17B50 |
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