On the uniform Poincaré inequality
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چکیده
We give a proof of the Poincaré inequality in W (Ω) with a constant that is independent of Ω ∈ U , where U is a set of uniformly bounded and uniformly Lipschitz domains in R. 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.
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تاریخ انتشار 2017