頁籤選單縮合
題 名 | Generalized Sharp Hardy Type and Caffarelli-Kohn-Nirenberg Type Inequalities on Riemannian Manifolds |
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作 者 | Wei, Walter Shihshu; Li, Ye; | 書刊名 | Tamkang Journal of Mathematics |
卷 期 | 40:4 2009.冬[民98.冬] |
頁 次 | 頁401-413 |
分類號 | 314.16 |
關鍵詞 | Caffarelli-Kohn-Nirenberg inequality; Hardy inequality; Radial curvature; Hessian comparison theorem; Sectional curvature; |
語 文 | 英文(English) |
英文摘要 | We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds M. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with compact support on the manifold M (that is, not necessarily on a punctured manifold M{x0} where x0 is a fixed point in M). Some topological and geometric applications are discussed. |
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