Homogenization of a quasi-linear problem with quadratic growth in perforated domains : an example
Estimate of the pressure when its gradient is the divergence of a measure. Applications
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . The proof is based partially on the Strauss inequality [Strauss, 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [ 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an...
Homogenization of systems with equi-integrable coefficients
In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions due to...
Results on existence of solution for an optimal design problem.
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.
Estimate of the pressure when its gradient is the divergence of a measure. Applications
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . The proof is based partially on the Strauss inequality [Strauss, (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [ (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of...
Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets
For a fixed bounded open set , a sequence of open sets and a sequence of sets , we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on , satisfying Neumann boundary conditions on and Dirichlet boundary conditions on . We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on and locally.
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