Best constant in critical Sobolev inequalities of second-order in the presence of symmetries
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 pro...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p689_Saintier |
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todo:paper_0362546X_v72_n2_p689_Saintier2023-10-03T15:27:23Z Best constant in critical Sobolev inequalities of second-order in the presence of symmetries Saintier, N. 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p689_Saintier |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Saintier, N. Best constant in critical Sobolev inequalities of second-order in the presence of symmetries |
| topic_facet |
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 |
| description |
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. |
| format |
JOUR |
| author |
Saintier, N. |
| author_facet |
Saintier, N. |
| author_sort |
Saintier, N. |
| title |
Best constant in critical Sobolev inequalities of second-order in the presence of symmetries |
| title_short |
Best constant in critical Sobolev inequalities of second-order in the presence of symmetries |
| title_full |
Best constant in critical Sobolev inequalities of second-order in the presence of symmetries |
| title_fullStr |
Best constant in critical Sobolev inequalities of second-order in the presence of symmetries |
| title_full_unstemmed |
Best constant in critical Sobolev inequalities of second-order in the presence of symmetries |
| title_sort |
best constant in critical sobolev inequalities of second-order in the presence of symmetries |
| url |
http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p689_Saintier |
| work_keys_str_mv |
AT saintiern bestconstantincriticalsobolevinequalitiesofsecondorderinthepresenceofsymmetries |
| _version_ |
1782030220790857728 |