Displaying similar documents to “The Euler equation for a class of nonconvex problems.”

Lower semicontinuity of multiple μ -quasiconvex integrals

Ilaria Fragalà (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Lower semicontinuity results are obtained for multiple integrals of the kind ∫ ℝ n f ( x , ∇ μ u ) d μ , where μ is a given positive measure on ℝ n , and the vector-valued function u belongs to the Sobolev space H μ 1 , p ( ℝ n , ℝ m ) associated with μ . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to μ . More precisely, for fully general μ , a notion of quasiconvexity for f along the tangent bundle to μ , turns out to be necessary...

On integral representation, relaxation and homogenization for unbounded functionals

Luciano Carbone, Riccardo De Arcangelis (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

A theory of integral representation, relaxation and homogenization for some types of variational functionals taking extended real values and possibly being not finite also on large classes of regular functions is presented. Some applications to gradient constrained relaxation and homogenization problems are given.