We present a unified strategy to derive Hardy-Poincare inequalities on bounded and unbounded domains. The approach allows proving a general Hardy-Poincare inequality from which the classical Poincare and Hardy inequalities immediately follow. We extend the idea to the more general context of variable exponent Sobolev spaces. Surprisingly, despite the well-known counterexamples of Fan et al. (2005) [28], we show that a modular form of the Poincare inequality is actually possible provided one restricts to the class of functions in u is an element of C-c(infinity)(omega) such that |u| & raquo; 5 1. The argument, concise and constructive, does not require a priori knowledge of compactness results and retrieves geometric information on the best constants. (C) 2022 Elsevier Inc. All rights reserved.
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