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Non-compactness and Multiplicity Results for the Yamabe Problem on Sn

โœ Scribed by Massimiliano Berti; Andrea Malchiodi

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
257 KB
Volume
180
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

The aim of this paper is to show the existence of metrics gร„ = on S n , where gร„ = is a perturbation of the standard metric gร„ 0 , for which the Yamabe problem possesses a sequence of solutions unbounded in L (S n ). The metrics gร„ = that we find are of class C k on S n with (k n&3 4 ). We also prove some new multiplicity results.

๐Ÿ“œ SIMILAR VOLUMES

A Multiplicity Result for the Yamabe Pro
A Multiplicity Result for the Yamabe Problem on Sn
โœ Antonio Ambrosetti; Andrea Malchiodi ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 213 KB

We prove a multiplicity result for the Yamabe problem on the manifold (S, g~), where g~is a perturbation of the standard metric g 0 of S n . Solutions are found by variational methods via an abstract perturbation result.

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We consider the p-Laplacian problem , where p u = div โˆ‡u p-2 โˆ‡u , ฮป is a constant in a certain range, and a โˆˆ L N/p โˆฉ L โˆž is nonnegative a โ‰ก 0. Using the principle of symmetric criticality, existence and multiplicity are proved under suitable conditions on a and f .

Existence and uniqueness results for the
Existence and uniqueness results for the non-autonomous coagulation and multiple-fragmentation equation
โœ D. J. McLaughlin; W. Lamb; A. C. McBride ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 154 KB ๐Ÿ‘ 2 views

An initial-value problem modelling coagulation and fragmentation processes is studied. The results of earlier papers are extended to models where either one or both of the rates of coagulation and fragmentation depend on time. An abstract integral equation, involving the solution operator to the lin