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Abstract:

We describe in this paper the asymptotic behaviour in Sobolev spaces of sequences of solutions of critical equations involving the p-Laplacian (see equations (E α) below) on a compact Riemannian manifold (M, g) which are invariant by a subgroup of the group of isometries of (M, g). We also prove pointwise estimates. © 2008 Birkhaueser.

Registro:

Documento: Artículo
Título:Blow-up theory for symmetric critical equations involving the p-Laplacian
Autor:Saintier, N.
Filiación:Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, (1428), Buenos Aires, Argentina
Palabras clave:Blow-up; Invariance under isometries; P-Laplacian
Año:2008
Volumen:15
Número:1-2
Página de inicio:227
Página de fin:245
DOI: http://dx.doi.org/10.1007/s00030-007-7006-8
Título revista:Nonlinear Differential Equations and Applications
Título revista abreviado:Nonlinear Diff. Equ. Appl.
ISSN:10219722
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v15_n1-2_p227_Saintier

Referencias:

  • BREDON, G.E., Introduction to compact transformation groups (1972) Academic Press, Pure and applied mathematics, 46
  • FAGET, Z., Best constant in Sobolev inequalities on Riemannian manifolds in the presence of symmetries (2002) Potential Analysis, 17 (2), pp. 105-124
  • FAGET, Z., Optimal constants in critical Sobolev inequalities on Riemannian manifolds in the presence of symmetries (2003) Ann. Global Anal. Geom, 24, pp. 161-200
  • HEBEY, E., Nonlinear analysis on manifolds: Sobolev spaces and inequalities (1999) Courant Lecture Notes in Mathematics, 5
  • HEBEY, E., ROBERT, F., Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients (2001) Calc. Var. Partial Differential Equations, 13 (4), pp. 491-517
  • HEBEY, E., VAUGON, M., Sobolev spaces in the presence of symmetries (1997) J. Math. Pures Appl, 76 (10), pp. 859-881
  • LIONS, P.L., The concentration-compactness principle in the calculus of variations, the limit case, parts 1 and 2 (1985) Rev.Mat.Iberoamericana, 1, pp. 145-201,45-121
  • ROBERT, F., Positive solutions for a fourth order equation invariant under isometries (2003) Proc. Amer. Math. Soc, 131 (5), pp. 1423-1431
  • SAINTIER, N., Asymptotic estimates and blow-up theory for critical equations involving the p-Laplacian (2006) Calc. Var. Partial Differential Equations, 25 (3), pp. 299-311
  • STRUWE, M., A global compactness result for elliptic boundary value problem involving limiting nonlinearities (1984) Math. Z, 187 (4), pp. 511-517
  • STRUWE, M., (2000) Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems, , Springer-Verlag, Berlin
  • TOLKSDORF, P., Regularity for a more general class of quasilinear elliptic equations (1984) J. Differential Equations, 51 (1), pp. 126-150
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Citas:

---------- APA ----------
(2008) . Blow-up theory for symmetric critical equations involving the p-Laplacian. Nonlinear Differential Equations and Applications, 15(1-2), 227-245.
http://dx.doi.org/10.1007/s00030-007-7006-8
---------- CHICAGO ----------
Saintier, N. "Blow-up theory for symmetric critical equations involving the p-Laplacian" . Nonlinear Differential Equations and Applications 15, no. 1-2 (2008) : 227-245.
http://dx.doi.org/10.1007/s00030-007-7006-8
---------- MLA ----------
Saintier, N. "Blow-up theory for symmetric critical equations involving the p-Laplacian" . Nonlinear Differential Equations and Applications, vol. 15, no. 1-2, 2008, pp. 227-245.
http://dx.doi.org/10.1007/s00030-007-7006-8
---------- VANCOUVER ----------
Saintier, N. Blow-up theory for symmetric critical equations involving the p-Laplacian. Nonlinear Diff. Equ. Appl. 2008;15(1-2):227-245.
http://dx.doi.org/10.1007/s00030-007-7006-8