The Concentration-Compactness Principle in the Calculus of Variations. (The limit case, Part. II.)

• Autores: Pierre-Louis Lions
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 1, Nº 2, 1985, págs. 45-121
• Idioma: inglés
• Títulos paralelos:
  • El principio de concentración-compacidad en el cálculo de variaciones. El caso límite, Parte II.
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• Resumen

  • 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. 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 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.