New weighted Hardy's inequalities with application to non-existence of\n global solutions

2012/07/16 by Daniel Hauer, Hauer, Daniel, Abdelaziz Rhandi +1
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1207.3587

Abstract

In this article, we prove a weighted Hardy inequality for 1<p<+\∞ and\ndimension d\≥1. If p>d, then we can deduce from our weighted Hardy\ninequality a Poincar 'e inequality. The proof of the weighted Hardy inequality\nis based on the method of vector fields firstly introduced by Mitidieri\n citeMR1769903. By the same method, we show for 1<p<+\∞ and d\≥1\nthat weighted Caffarelli-Kohn-Nirenberg inequalities hold true. As an\napplication of our weighted Hardy inequality, we prove a non-existence result\nfor a p-Kolmogorov parabolic equation.\n

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