Improved 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...
متن کاملPoincaré Inequalities in Punctured Domains 1069
The classic Poincaré inequality bounds the Lq-norm of a function f in a bounded domain Ω ⊂ Rn in terms of some Lp-norm of its gradient in Ω. We generalize this in two ways: In the first generalization we remove a set Γ from Ω and concentrate our attention on Λ = Ω \ Γ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it, or if it does hold it m...
متن کاملSOBOLEV - POINCARÉ INEQUALITIES FOR p < 1
If Ω is a John domain (or certain more general domains), and |∇u| satisfies a certain mild condition, we show that u ∈ W 1,1 loc (Ω) satisfies a Sobolev-Poincaré inequality`R Ω |u − a| q ´ 1/q ≤ C `R Ω |∇u| p ´ 1/p for all 0 < p < 1, and appropriate q > 0. Our conclusion is new even when Ω is a ball.
متن کاملElliptic Complexes and Generalized Poincaré Inequalities
We study first order differential operators P = P(D) with constant coefficients. The main question is under what conditions a generalized Poincaré inequality holds D(f − f 0) L p ≤ C Pf L p , for some f 0 ∈ ker P. We show that the constant rank condition is sufficient, Theorem 3.5. The concept of the Moore-Penrose generalized inverse of a matrix comes into play.
متن کاملPoincaré inequalities for inhomogeneous Bernoulli measures
Recently there has been a lot of interest in the transport properties of particle systems in random media [AHL, BE, F, GP, KPW, K, MA, R, Se]. A simple model for which the hydrodynamic scaling limit can be obtained is the Kawasaki dynamics for random Bernoulli measures [Q], [QY]. Such systems have been used to model electron transport in doped crystals. The hydrodynamic limit is a nonlinear dif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2012
ISSN: 0362-546X
DOI: 10.1016/j.na.2012.05.008