Extremal functions for the sharp L− Nash inequality
نویسنده
چکیده
منابع مشابه
Extremal functions for the sharp L2− Nash inequality
This paper is in the spirit of several works on best constants problems in Sobolev type inequalities. A general reference on this subject is the recent book of Hebey [9]. These questions have many interests. At first, they are at the origin of the resolution of famous geometrical problems as Yamabe problem. More generally, they show how geometry and analysis interact on Riemannian manifolds and...
متن کاملSharp Constant and Extremal Function for the Improved Moser-trudinger Inequality Involving L Norm in Two Dimension
Let Ω ⊂ R 2 be a smooth bounded domain, and H 1 0 (Ω) be the standard Sobolev space. Define for any p > 1, λp(Ω) = inf u∈H 1 0 (Ω),u ≡0 ∇u 2 2 /u 2 p , where · p denotes L p norm. We derive in this paper a sharp form of the following improved Moser-Trudinger inequality involving the L p-norm using the method of blow-up analysis: sup u∈H 1 0 (Ω),∇u 2 =1 Ω e 4π(1+αu 2 p)u 2 dx < +∞ for 0 ≤ α < λp...
متن کاملSharp Hardy-littlewood-sobolev Inequality on the Upper Half Space
There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent λ = n−α (that is for the case of α > n). In this paper we confirm the possibility for the extension along the first direction by establishing the sharp Hardy-Littlewood-Sobolev inequ...
متن کاملSome Extremal Problems for Analytic Functions
The paper mainly concerns with functions f , analytic in S : |Imz| < 1 and bounded by a constant M > 1. We state sharp estimates for supR |f ′| under the additional condition supR |f | ≤ 1. Using these estimates we deduce well-known Bernstein’s inequality and some its generalizations for entire functions of a finite type with respect to an arbitrary proximate order. Parallely we investigate als...
متن کاملSharp 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017