Improved Poincare inequalities with weights

In this paper we prove that if Omega is an element of R-n is a bounded John domain, the following weighted Poincare-type inequality holds: [GRAPHICS] where f is a locally Lipschitz function on Omega, d(x) denotes the distance of x to the boundary of Omega, the weights W-1, W-2 satisfy certain cube conditions, and alpha is an element of [0, 1] depends on p, q and n. This result generalizes previously known weighted inequalities, which can also be obtained with our approach. (c) 2008 Elsevier Inc. All rights reserved.