The second Yamabe invariant with singularities (Q443800)
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scientific article; zbMATH DE number 6065094
| Language | Label | Description | Also known as |
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| English | The second Yamabe invariant with singularities |
scientific article; zbMATH DE number 6065094 |
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The second Yamabe invariant with singularities (English)
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13 August 2012
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The paper concerns the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics of volume 1 (see also [\textit{T. Aubin}, J. Math. pur. appl., IX. Sér. 55, 269--296 (1976; Zbl 0336.53033); \textit{F. Madani}, Bull. Sci. Math. 132, No. 7, 575--591 (2008; Zbl 1152.58017)]). It is shown that this operator is attained by a generic metric. Nodal solutions to a Yamabe type equation with singularities are deduced.
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second Yamabe invariant
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singularities
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critical Sobolev growth
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