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

Pierre-Louis Lions

Revista Matemática Iberoamericana (1985)

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

Abstract

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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 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.

How to cite

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Lions, 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 -

Citations in EuDML Documents

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  1. Pedro Girão, Miguel Ramos, Sign changing solutions for elliptic equations with critical growth in cylinder type domains
  2. James W. Dold, Victor A. Galaktionov, Andrew A. Lacey, Juan Luis Vázquez, Rate of approach to a singular steady state in quasilinear reaction-diffusion equations
  3. Pedro Girão, Miguel Ramos, Sign changing solutions for elliptic equations with critical growth in cylinder type domains
  4. Bruno Nazaret, Stability results for some nonlinear elliptic equations involving the p -laplacian with critical Sobolev growth
  5. Morgan Pierre, Newton and conjugate gradient for harmonic maps from the disc into the sphere
  6. Fengbo Hang, Xiaodong Wang, Xiaodong Yan, An integral equation in conformal geometry
  7. Stefan Müller, Michael Struwe, Vladimir Šverák, Harmonic maps on planar lattices
  8. Bruno Nazaret, Stability results for some nonlinear elliptic equations involving the -Laplacian with critical Sobolev growth
  9. Morgan Pierre, Newton and conjugate gradient for harmonic maps from the disc into the sphere
  10. Michael Struwe, Recent existence and regularity results for wave maps

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