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A Generalization of an Inequality of Bhattacharya and Leonetti
Published online by Cambridge University Press: 20 November 2018
Abstract
We show that bounded John domains and bounded starshaped domains with respect to a point satisfy the following inequality
where F: [0, ∞) → [0, ∞) is a continuous, convex function with F(0) = 0, and u is a function from an appropriate Sobolev class. Constants b and K do depend at most on D. If F(x) = xp, 1 ≤ p < ∞, this inequality reduces to the ordinary Poincaré inequality.
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- Copyright © Canadian Mathematical Society 1996
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