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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2009
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v72_n2_p689_Saintier http://hdl.handle.net/20.500.12110/paper_0362546X_v72_n2_p689_Saintier |
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| Sumario: | 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. |
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