Sharp constant in a sobolev trace inequality
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, … WebbThe 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 …
Sharp constant in a sobolev trace inequality
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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), ... WebbSHARP 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 …
Webb15 nov. 2006 · Actually, since the proof applies for any norm on R + n, it generalizes in the case p = 2 the result of [15] and [4], showing that neither conformal invariance nor the … Webb12 apr. 2024 · PDF We give an overview of our recent new proof of the Riemannian Penrose inequality in the case of a single black hole. The proof is based on a new... Find, read and cite all the research you ...
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 assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy–Sobolev–Maz’ya inequalities with best Hardy constants for various fractional … 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...
Webb8 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 …
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 ... react location inputWebb1 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, ... react localstorage getitem useeffectWebbWith SHARP's scientific calculators, the figures you omit are automatically shown as K (constant) or ANS (answer). Contradictions between equations and answers are … react locomotive scrollWebbStatement 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, ‖ ‖ ‖ ‖ (). ... react lockWebbThe 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] ... react lodash throttleWebb1 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 … react lock scrollWebbThere is, however, a type of Sobolev inequality, established by Leonard Gross ( Gross 1975) and known as a logarithmic Sobolev inequality, that has dimension-independent … react location.search