منابع مشابه
On the Yamabe Equation with Rough Potentials
We study the existence of non–trivial solutions to the Yamabe equation: −∆u+ a(x) = μu|u| 4 n−2 μ > 0, x ∈ Ω ⊂ R with n ≥ 4, u(x) = 0 on ∂Ω under weak regularity assumptions on the potential a(x). More precisely in dimension n ≥ 5 we assume that: (1) a(x) belongs to the Lorentz space L n 2 (Ω) for some 1 ≤ d < ∞, (2) a(x) ≤ M < ∞ a.e. x ∈ Ω, (3) the set {x ∈ Ω|a(x) < 0} has positive measure, (4...
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We show a conformal spectral estimate for the Dirac operator on a non-conformally-flat Riemannian spin manifolds of dimension n ≥ 7. The estimate is a spinorial analogue to an estimate by Aubin which solved the Yamabe problem for the above manifolds. Using Hijazi’s inequality our estimate implies Aubin’s estimate. More exactly, let M be a compact manifold of dimension n ≥ 7 equipped with a Riem...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13929