Sharp Sobolev inequalities involving boundary terms revisited
نویسندگان
چکیده
We revisit the sharp Sobolev inequalities involving boundary terms on Riemannian manifolds with boundaries proved by Li and Zhu (Geom Funct Anal 8: 59–87, 1998) explore role of mean curvature.
منابع مشابه
Sharp Sobolev inequalities involving boundary terms
Let (M, g) be a compact Riemannian manifold of dimension n (n ≥ 3) with smooth boundary. In [LZ], we established some sharp trace inequality on (M, g). In this paper we establish some sharp Sobolev inequalities using the method in [LZ]. For n ≥ 3, it was shown by Aubin [Au1] and Talenti [T] that, for p = 2n/(n − 2), 1 S 1 = inf R n |∇u| 2 R n |u| p 2/p u ∈ L p (R n) \ {0}, ∇u ∈ L 2 (R n) , (0.1...
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ژورنال
عنوان ژورنال: Calculus of Variations and Partial Differential Equations
سال: 2021
ISSN: ['0944-2669', '1432-0835']
DOI: https://doi.org/10.1007/s00526-021-02036-z