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Abstract:

Let (M, g) be a smooth compact Riemannian manifold. We first give the value of the best first constant for the critical embedding H2 (M) {right arrow, hooked} L2{music sharp sign} (M) for second-order Sobolev spaces of functions invariant by some subgroup of the isometry group of (M, g). We also prove that we can take ε{lunate} = 0 in the corresponding inequality under some geometric assumptions. As an application we give a sufficient condition for the existence of a smooth positive symmetric solution to a critical equation with a symmetric Paneitz-Branson-type operator. A sufficient condition for the existence of a nodal solution to such an equation is also derived. We eventually prove a multiplicity result for such an equation. © 2009 Elsevier Ltd. All rights reserved.

Registro:

Documento: Artículo
Título:Best constant in critical Sobolev inequalities of second-order in the presence of symmetries
Autor:Saintier, N.
Filiación:Departamento de Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, C.P. 1613 Los Polvorines, Pcia de Bs. As., Argentina
Palabras clave:Best constant; BiLaplacian; Invariance under isometries; Paneitz-type operator; Best constant; Best constants; Multiplicity results; Nodal solutions; Riemannian manifold; Second orders; Sobolev inequalities; Sobolev space; Sufficient conditions; Symmetric solution; Fluorine containing polymers; Mathematical operators
Año:2009
Volumen:72
Número:2
Página de inicio:689
Página de fin:703
DOI: http://dx.doi.org/10.1016/j.na.2009.07.010
Título revista:Nonlinear Analysis, Theory, Methods and Applications
Título revista abreviado:Nonlinear Anal Theory Methods Appl
ISSN:0362546X
CODEN:NOAND
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v72_n2_p689_Saintier

Referencias:

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Citas:

---------- APA ----------
(2009) . Best constant in critical Sobolev inequalities of second-order in the presence of symmetries. Nonlinear Analysis, Theory, Methods and Applications, 72(2), 689-703.
http://dx.doi.org/10.1016/j.na.2009.07.010
---------- CHICAGO ----------
Saintier, N. "Best constant in critical Sobolev inequalities of second-order in the presence of symmetries" . Nonlinear Analysis, Theory, Methods and Applications 72, no. 2 (2009) : 689-703.
http://dx.doi.org/10.1016/j.na.2009.07.010
---------- MLA ----------
Saintier, N. "Best constant in critical Sobolev inequalities of second-order in the presence of symmetries" . Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 2, 2009, pp. 689-703.
http://dx.doi.org/10.1016/j.na.2009.07.010
---------- VANCOUVER ----------
Saintier, N. Best constant in critical Sobolev inequalities of second-order in the presence of symmetries. Nonlinear Anal Theory Methods Appl. 2009;72(2):689-703.
http://dx.doi.org/10.1016/j.na.2009.07.010