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Homogenization of non-uniformly bounded periodic diffusion energies in dimension two

 

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Opened Access Homogenization of non-uniformly bounded periodic diffusion energies in dimension two
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Author: Braides, Andrea
Briane, Marc
Casado Díaz, Juan
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2009
Published in: Nonlinearity, 22, 1459-1480.
Document type: Article
Abstract: This paper deals with the homogenization of two-dimensional oscillating convex functionals, the densities of which are equicoercive but not uniformly bounded from above. Using a uniform-convergence result for the minimizers, which holds for this type of scalar problems in dimension two, we prove in particular that the limit energy is local and recover the validity of the analogue of the well-known periodic homogenization formula in this degenerate case. However, in the present context the classical argument leading to integral representation based on the use of cut-off functions is useless due to the unboundedness of the densities. In its place we build sequences with bounded energy, which converge uniformly to piecewise-affine functions, taking pointwise extrema of recovery sequences for affine functions.
Cite: Braides, A., Briane, M. y Casado Díaz, J. (2009). Homogenization of non-uniformly bounded periodic diffusion energies in dimension two. Nonlinearity, 22, 1459-1480.
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URI: http://hdl.handle.net/11441/47811

DOI: 10.1088/0951-7715/22/6/010

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