Sharp constant in a sobolev trace inequality
Webb1 feb. 1993 · Sharp constant in a Sobolev inequality. Mathematics of computing. Mathematical analysis. Differential equations. Partial differential equations. Comments. Login options. Check if you have access through your login ... 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
Sharp constant in a sobolev trace inequality
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WebbThe trace theorem of Sobolev spaces on Lipschitz domains is as follows. Theorem 1. LetΩbe a bounded simply connected Lipschitz domain and1 2< s<3 2 Then the trace operator γj @Ωis a bounded linear operator from H s(Ω) to Hs−1 2(@Ω). Before we prove this theorem, we need to establish several lemmas. De nition 5. Webb13 apr. 2024 · On the generalized Grushin plane, Liu obtained some sharp trace and isocapacity inequalities via the BV-capacity. We refer the reader to [19 , 23, ... There exists a positive constant \(C_1\) such that for all compact sets \(K\subseteq \mathbb R ... The sharp Sobolev and isoperimetric inequalities split twice. Adv. Math. 211(2), ...
WebbW. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality. Annals of Mathematics 138, No. 1 (1993), 213–242 Google Scholar J.P. Bourguignon, J.P. Ezin, Scalar Curvature Functions in a Conformal Class of Metrics and Conformal transformations. Trans. Amer. Mat. Soc. 301 (1987), 723–736 Google Scholar Webb8 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 …
Webb1 dec. 2012 · The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains Ω ⊂ ℝn is shown to agree with an isoperimetric constant associated with Ω. The... 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...
WebbWe establish three families of Sobolev trace inequalities of orders two and four in the unit ball under higher order moments constraint, and are able to construct smooth test …
WebbThe first sharp Sobolev trace inequality was proven by Escobar[21]. ... Obata-type argument which classifies all conformally flat,scalar flat metrics g on the ball for which the boundary has constant mean curvature. The inequality (1.1) plays a crucial role in studying a version of the boundary Yamabe problem;see[2,22,31–33] ... ordering from harbor freight onlineWebbThere is, however, a type of Sobolev inequality, established by Leonard Gross ( Gross 1975) and known as a logarithmic Sobolev inequality, that has dimension-independent … irenes rythm current positionWebbQuick Search in Journals. Enter Search Terms Search. Quick Search anywhere irenes wave 2143nWebbfor all , , , 0 ordering from thomann to usaWebbTrace. Sharp constants in ... 11 IXI - * fIq < Np f A , Iif IIwith Nbeing the sharp constant and i/p + X/n = 1 + 1/q, 1 irenes photo port orchardWebba 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. ordering from the eu to ukWebb8 maj 2024 · We establish a sharp affine L^p Sobolev trace inequality by using the L_p Busemann–Petty centroid inequality. For p = 2, our affine version is stronger than the … irenes shop