JournalsrmiVol. 1, No. 2pp. 45–121

The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 2

  • Pierre-Louis Lions

    Université de Paris-Dauphine, Paris, France
The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 2 cover
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Abstract

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 RN\mathbb R^N. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sovolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle and method introduced in the so-called locally compact case are to be modified in order to solve these problems and we present applications to Functional Analysis, Mathematical Physics, Differential Geometry and Harmonic Analysis.

Cite this article

Pierre-Louis Lions, The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 2. Rev. Mat. Iberoam. 1 (1985), no. 2, pp. 45–121

DOI 10.4171/RMI/12