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arXiv · 1207.3587

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

Daniel Hauer·Abdelaziz Rhandi
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Abstract

In this article, we prove a weighted Hardy inequality for $1 d$, then we can deduce from our weighted Hardy inequality a Poincaré inequality. The proof of the weighted Hardy inequality is based on the method of vector fields firstly introduced by Mitidieri \cite{MR1769903}. By the same method, we show for $1<p<+\infty$ and $d\ge1$ that weighted Caffarelli-Kohn-Nirenberg inequalities hold true. As an application of our weighted Hardy inequality, we prove a non-existence result for a p-Kolmogorov parabolic equation.

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Daniel Hauer, Abdelaziz Rhandi. 2012-07-19. New weighted Hardy's inequalities with application to non-existence of global solutions. https://arxiv.org/abs/1207.3587

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