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

Revista Matemática Iberoamericana (1985)

- Volume: 1, Issue: 1, page 145-201
- ISSN: 0213-2230

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topLions, Pierre-Louis. "The concentration-compactness principle in the calculus of variations. The limit case, Part I.." Revista Matemática Iberoamericana 1.1 (1985): 145-201. <http://eudml.org/doc/39314>.

@article{Lions1985,

abstract = {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 RN where the invariance of RN 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 principle has to be modified in order to be able to treat this class of 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; Minimización; functional inequalities; Sobolev inequalities; concentration-compactness principle},

language = {eng},

number = {1},

pages = {145-201},

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

url = {http://eudml.org/doc/39314},

volume = {1},

year = {1985},

}

TY - JOUR

AU - Lions, Pierre-Louis

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

JO - Revista Matemática Iberoamericana

PY - 1985

VL - 1

IS - 1

SP - 145

EP - 201

AB - 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 RN where the invariance of RN 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 principle has to be modified in order to be able to treat this class of 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; Minimización; functional inequalities; Sobolev inequalities; concentration-compactness principle

UR - http://eudml.org/doc/39314

ER -

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