On the Uniform Poincaré Inequality
Authors:
- 5 September 2007
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 32 (9) , 1439-1447
Abstract
We give a proof of the Poincaré inequality in W 1, p (Ω) with a constant that is independent of Ω ∊ , where is a set of uniformly bounded and uniformly Lipschitz domains in ℝ n . As a byproduct, we obtain the following: The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the domains Ω vary and remain uniformly bounded and uniformly Lipschitz regular.Keywords
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