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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 3, 2003, pp. 591–608
DOI: 10.4171/ZAA/1164

Published online: 2003-09-30

Homogenization of Dirichlet Problems with Convex Bounded Constraints on the Gradient

Thierry Champion[1] and Luigi De Pascale[2]

(1) Université de Toulon et du Var, La Garde, France
(2) Università di Pisa, Italy

We give a simpler proof of a conjecture of A. Bensoussan, J. L. Lions and G. Papanicolaou on the homogenization of Dirichlet problems with convex bounded constraints on the gradient. Our proof is based on a regularization technique for the constrained functionals as well as on a fine approximation technique.

Keywords: Homogenization, Moreau-Yosida approximation, convex constraints on the gradients

Champion Thierry, De Pascale Luigi: Homogenization of Dirichlet Problems with Convex Bounded Constraints on the Gradient. Z. Anal. Anwend. 22 (2003), 591-608. doi: 10.4171/ZAA/1164