On the best constant of weighted Poincaré inequalities
نویسندگان
چکیده
منابع مشابه
On Friedrichs – Poincaré - type inequalities ✩
Friedrichsand Poincaré-type inequalities are important and widely used in the area of partial differential equations and numerical analysis. Most of their proofs appearing in references are the argument of reduction to absurdity. In this paper, we give direct proofs of Friedrichs-type inequalities in H 1(Ω) and Poincaré-type inequalities in some subspaces of W1,p(Ω). The dependencies of the ine...
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Abstract. We prove Poincaré and Plancherel–Polya inequalities for weighted p-spaces on weighted graphs in which the constants are explicitly expressed in terms of some geometric characteristics of a graph. We use a Poincaré-type inequality to obtain some new relations between geometric and spectral properties of the combinatorial Laplace operator. Several well-known graphs are considered to dem...
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when 0 < s < 2, 2 := 2∗(s) = 2(n−s) n−2 , and when 0 is on the boundary ∂Ω. This question is closely related to the geometry of ∂Ω, as we extend here the main result obtained in [15] by proving that at least in dimension n ≥ 4, the negativity of the mean curvature of ∂Ω at 0 is sufficient to ensure the attainability of μs(Ω). Key ingredients in our proof are the identification of symmetries enj...
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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولSUBELLIPTIC POINCARÉ INEQUALITIES : THE CASE p < 1
We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for p < 1 under some assumptions on the subelliptic gradient of the function. Such inequalities hold on Boman domains associated with the underlying CarnotCarathéodory metric. In particular, they remain true for solutions to certain classes of subelliptic equations. Our results complement the ea...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.10.027