Relaxation of singular functionals defined on Sobolev spaces
Hafedh Ben Belgacem (2000)
ESAIM: Control, Optimisation and Calculus of Variations
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Displaying similar documents to “Relaxation theorems in nonlinear elasticity”
Relaxation of singular functionals defined on Sobolev spaces
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We consider the lower semicontinuous functional of the form where satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar’s -convexity condition for the integrand extends to the new geometric conditions satisfied on four dimensional symplexes. Similar conditions on three dimensional symplexes were recently obtained by the second author. New conditions apply...
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Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna [ (1999) 185–206]. For energies with superlinear or linear growth, a -convergence result is established in Sobolev spaces, the homogenization problem in the space of functions of bounded variation being the object of...