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

Revista Matemática Iberoamericana (1985)

- Volume: 1, Issue: 2, page 45-121
- ISSN: 0213-2230

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topLions, Pierre-Louis. "The concentration-compactness principle in the calculus of variations. The limit case, Part II.." Revista Matemática Iberoamericana 1.2 (1985): 45-121. <http://eudml.org/doc/39321>.

@article{Lions1985,

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. 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.},

author = {Lions, Pierre-Louis},

journal = {Revista Matemática Iberoamericana},

keywords = {Cálculo de variaciones; Principio de concentración-compacidad; Teoría de Morse; Dominios no acotados; Masas de Dirac; Grupo de invariancias; Teoremas de trazas; Sobolev inequalities; convolution or trace inequalities; concentration- compactness principle},

language = {eng},

number = {2},

pages = {45-121},

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

url = {http://eudml.org/doc/39321},

volume = {1},

year = {1985},

}

TY - JOUR

AU - Lions, Pierre-Louis

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

JO - Revista Matemática Iberoamericana

PY - 1985

VL - 1

IS - 2

SP - 45

EP - 121

AB - 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.

LA - eng

KW - Cálculo de variaciones; Principio de concentración-compacidad; Teoría de Morse; Dominios no acotados; Masas de Dirac; Grupo de invariancias; Teoremas de trazas; Sobolev inequalities; convolution or trace inequalities; concentration- compactness principle

UR - http://eudml.org/doc/39321

ER -

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