Sharp constant in a sobolev trace inequality
WebbLOGARITHMIC SOBOLEV TRACE INEQUALITY YOUNG JA PARK (Communicated by Andreas Seeger) Abstract. A logarithmic Sobolev trace inequality is derived. Bounds on …
Sharp constant in a sobolev trace inequality
Did you know?
Webb21 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 … Webb10 okt. 2014 · Nazaret, B., Best constant in Sobolev trace inequalities on the half-space. ... The sharp Sobolev type inequalities in the Lorentz–Sobolev spaces in the hyperbolic spaces. Journal of Mathematical Analysis and Applications, Vol. 490, Issue. 1, …
Webb1 maj 1997 · A SHARP SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS∗ A. U.S Mathematics 2003 Let (M, g) be a smooth compact Riemannian manifold without … WebbStatement of the inequality The classical Poincaré inequality. Let p, so that 1 ≤ p < ∞ and Ω a subset bounded at least in one direction.Then there exists a constant C, depending only on Ω and p, so that, for every function u of the Sobolev space W 0 1,p (Ω) of zero-trace (a.k.a. zero on the boundary) functions, ‖ ‖ ‖ ‖ (). ...
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. Webb15 nov. 2006 · In [20], Maggi and Villani proved an optimal inequality valid on all locally Lipschitz domains : (10) where (this exponent is the critical one for the Sobolev embedding into space on the boundary), and is the isoperimetric constant. In addition, they showed that (10) is sharp on balls. This generalizes in particular a result of Brezis and Lieb ...
Webb1 aug. 2003 · The best Sobolev trace constant is given by the first eigenvalue of a Steklov-like problem. ... In this paper, we establish some sharp Sobolev trace inequalities on n-dimensional, ...
Webb27 nov. 2012 · The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains Ω ⊂ ℝ n is shown to agree with an isoperimetric … job search help montrealWebb13 apr. 2024 · In a celebrated work [], Bourgain, Brezis and Mironescu study the asymptotic behavior of the fractional Sobolev seminorms when the order of differentiability approaches one.Their results are concerned with smooth bounded domains, but the same arguments work for \(W^{1, p}\)-extension domain.More precisely, if \(\Omega \subset … insulin for diabetic tertiaryWebbThe following sharp Sobolev embedding theorem then follows immediately. Theorem 1.3. (see Theorem 3.1 below) Let B0 ⊂ X be a ball, and let Y(X) be an r.i. space. Suppose that … job search help in torontoWebbSHARP TRACE INEQUALITY 6753 procedure to prove those types of inequalities is by contradiction. A key point is to derive the asymptotical behavior of extremal functions … job search help minneapolisWebba 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. insulin for dogs best priceWebb1 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 ... job search help nycWebb19 juli 2024 · Almost sharp Sobolev trace inequalities in the unit ball under constraints. Xuezhang Chen, Wei Wei, Nan Wu. We establish three families of Sobolev trace … job search help san antonio