Displaying similar documents to “Existence and regularity of minima for integral functionals noncoercive in the energy space”

The summability of solutions to variational problems since Guido Stampacchia.

Lucio Boccardo (2003)

RACSAM

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Inequalities concerning the integral of |∇u| on the subsets where |u(x)| is greater than k can be used in order to prove regularity properties of the function u. This method was introduced by Ennio De Giorgi e Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems.

The concentration-compactness principle in the calculus of variations. The limit case, Part II.

Pierre-Louis Lions (1985)

Revista Matemática Iberoamericana

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This paper is the second part of a work devoted to the study of variational problems (with constraints) in functional spaces defined on domains presenting some (local) form of invariance by a non-compact group of transformations like the dilations in R. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sobolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle...

The concentration-compactness principle in the calculus of variations. The limit case, Part I.

Pierre-Louis Lions (1985)

Revista Matemática Iberoamericana

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After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in R where the invariance of R by the group of dilatations creates some possible loss of compactness. This is for example the case for all the problems associated with the determination of extremal functions in functional inequalities (like for example the Sobolev inequalities). We show here how the concentration-compactness...