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Hardy Inequalities for Finsler p-Laplacian in the Exterior Domain

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Abstract

The Finsler p-Laplacian is the class of nonlinear differential operators given by

$$\begin{aligned} \Delta _{H,p}u:= \text {div}(H(\nabla u)^{p-1}\nabla _{\eta } H(\nabla u)) \end{aligned}$$

where \(1<p<\infty \) and \(H:\mathbf {R}^N\rightarrow [0,\infty )\) is in \(C^2(\mathbf {R}^N\backslash \{0\})\) and is positively homogeneous of degree 1. Under some additional constraints on H, we derive the Hardy inequality for Finsler p-Laplacian in exterior domain for \(1<p\le N\). We also provide an improved version of Hardy inequality for the case \(p=2\).

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  1. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India

    Kaushik Bal

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  1. Kaushik Bal
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Bal, K. Hardy Inequalities for Finsler p-Laplacian in the Exterior Domain. Mediterr. J. Math. 14, 165 (2017). https://doi.org/10.1007/s00009-017-0966-y

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  • DOI: https://doi.org/10.1007/s00009-017-0966-y

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