Displaying similar documents to “Equi-integrability results for 3D-2D dimension reduction problems”

Homogenization of variational problems in manifold valued Sobolev spaces

Jean-François Babadjian, Vincent Millot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

On a class of nonlinear problems involving a p ( x ) -Laplace type operator

Mihai Mihăilescu (2008)

Czechoslovak Mathematical Journal

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We study the boundary value problem - d i v ( ( | ∇ u | p 1 ( x ) - 2 + | ∇ u | p 2 ( x ) - 2 ) ∇ u ) = f ( x , u ) in Ω , u = 0 on ∂ Ω , where Ω is a smooth bounded domain in ℝ N . Our attention is focused on two cases when f ( x , u ) = ± ( - λ | u | m ( x ) - 2 u + | u | q ( x ) - 2 u ) , where m ( x ) = max { p 1 ( x ) , p 2 ( x ) } for any x ∈ Ω ¯ or m ( x ) < q ( x ) < N · m ( x ) ( N - m ( x ) ) for any x ∈ Ω ¯ . In the former case we show the existence of infinitely many weak solutions for any λ > 0 . In the latter we prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a ℤ 2 -symmetric version for even...