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Asymptotic behavior of nonlinear systemsin varying domains with boundary conditions on varying sets
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 1 / January 2009
- Published online by Cambridge University Press:
- 23 January 2009, pp. 49-67
- Print publication:
- January 2009
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- Article
- Export citation
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For a fixed bounded open set $\Omega\subset\mathbb{R}^N$
, a sequence of open sets $\Omega_n\subset\Omega$ 
and a sequence of sets $\Gamma_n\subset\partial\Omega\cap\partial\Omega_n$ 
, we study theasymptotic behavior of the solution of a nonlinear ellipticsystem posed on $\Omega_n$ 
, satisfying Neumann boundary conditionson $\Gamma_n$ 
and Dirichlet boundary conditions on $\partial\Omega_n\setminus \Gamma_n$ 
. We obtain a representationof the limit problem which is stable by homogenization and weprove that this representation depends on $\Omega_n$ and $\Gamma_n$ locally.
