Sharp constant in a sobolev trace inequality
WebbQuick Search in Journals. Enter Search Terms Search. Quick Search anywhere WebbThus, the inequality (1) takes the form of a Sobolev inequality for fractional derivatives Cn(g, √ −∆g) ≥ kgk2 L 2(n−1) n−2 (Rn−1, (7) for which Lieb’s sharp HLS inequality ([5]) yields the sharp constant, including all the cases of equality. Another important approach to Escobar’s inequality is based on transportation theory [7].
Sharp constant in a sobolev trace inequality
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WebbThe sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on R n, and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb’s sharp form of the Hardy-Littlewood-Sobolev inequality. References Similar Articles Additional Information Webba Sobolev inequality which holds on every submanifold in Euclidean space (see [1], Section 7, and [14]). This inequality is particularly useful on a minimal submanifold; in general, it contains a term involving the mean curvature. The constant in the Michael-Simon Sobolev inequality depends only on the dimension; however, the constant is not sharp.
Webb9 juli 2001 · The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the …
WebbThe inequality is sharp in the sense that the inequality is false whenSis replaced by any smaller number.c 1997 John Wiley & Sons, Inc. 0 Introduction It is well-known that sharp … Webb1 aug. 2003 · From this inequality, several other Sobolev-type trace inequalities follow: using a standard contradiction argument, one can for instance show that there exists a …
Webb19 sep. 2013 · Given (M, g) a smooth compact Riemannian n-manifold, n ≥ 3, we return in this article to the study of the sharp Sobolev-Poincaré type inequality (0.1) ∥u∥2*2 ≤ …
Webb1 dec. 1976 · The best constant for the simplest Sobolev inequality is exhibited. The proof is accomplished by symmetrizations (rearrangements in the sense of Hardy-Littlewood) and one-dimensional calculus... how many cheat meals should you haveWebb8 sep. 2015 · 1 Answer. The term sharp means we can find a best bound, that cannot be improved by a better number. I.e., to say a function is bounded is to say there exists an … how many chats can be pinned in whatsappWebb1 dec. 2024 · The main purpose of this paper is to establish trace Hardy-Sobolev-Maz'ya inequalities on half space. In case n = 2, we show that the sharp constant coincides with the best trace Sobolev constant.This is an analogous result to that of the sharp constant in the n − 1 2-th order Hardy-Sobolev-Maz'ya inequality in the half space of dimension n … high school football streaming liveWebb28 mars 2016 · arXiv:1603.07792v1 [math.FA] 25 Mar 2016 SometraceHardytypeinequalitiesandtrace Hardy-Sobolev-Maz’yatypeinequalities Van Hoang Nguyen∗ March 28, 2016 Abstract ... how many cheat days can i haveWebbTrace. Sharp constants in ... 11 IXI - * fIq < Np f A , Iif IIwith Nbeing the sharp constant and i/p + X/n = 1 + 1/q, 1 high school football targeting ruleWebb1. LOGARITHMIC SOBOLEV TRACE INEQUALITY A logarithmic Sobolev trace inequality will be derived from the sharp Sobolev trace inequality, and by doing so one can recognize it as a limiting case of the classical Sobolev trace inequalities. Theorem 1. For f E S(IR") with f flIL2(Rn) = 1 and n > 1, (3) j f(x)l2 lnIf(x)ldx < In AAn IVu(x,y) 2dxd Rn 2 ... how many cheaters are in tarkovWebb21 nov. 2012 · In this work we establish trace Hardy and trace Hardy–Sobolev–Maz’ya inequalities with best Hardy constants for domains satisfying suitable geometric … how many cheaters are in csgo