COMPACTNESS AND GLOBAL ESTIMATES FOR A FOURTH ORDER EQUATION OF CRITICAL SOBOLEV GROWTH ARISING FROM CONFORMAL GEOMETRY
2006 ◽
Vol 08
(01)
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pp. 9-65
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Keyword(s):
Given (M,g) a smooth compact Riemannian manifold of dimension n ≥ 5, we investigate compactness for fourth order critical equations like Pgu = u2♯-1, where [Formula: see text] is a Paneitz–Branson operator with constant coefficients b and c, u is required to be positive, and [Formula: see text] is critical from the Sobolev viewpoint. We prove that such equations are compact on locally conformally flat manifolds, unless b lies in some closed interval associated to the spectrum of the smooth symmetric (2,0)-tensor field involved in the definition of the geometric Paneitz–Branson operator.
2015 ◽
Vol 421
(1)
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pp. 893-904
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Keyword(s):
2014 ◽
Vol 98
(2)
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pp. 349-356
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2018 ◽
Vol 146
(12)
◽
pp. 5367-5378
2006 ◽
Vol 26
(3)
◽
pp. 343-356
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2017 ◽
Vol 42
(9)
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pp. 1481-1496
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Keyword(s):