# Hardy Inequalities for Finsler p-Laplacian in the Exterior Domain

Hardy Inequalities for Finsler p-Laplacian in the Exterior Domain 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} Δ H , p u : = div ( H ( ∇ u ) p - 1 ∇ η H ( ∇ u ) ) where $$1<p<\infty$$ 1 < p < ∞ and $$H:\mathbf {R}^N\rightarrow [0,\infty )$$ H : R N → [ 0 , ∞ ) is in $$C^2(\mathbf {R}^N\backslash \{0\})$$ C 2 ( R N \ { 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 $$1<p\le N$$ 1 < p ≤ N . We also provide an improved version of Hardy inequality for the case $$p=2$$ p = 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# Hardy Inequalities for Finsler p-Laplacian in the Exterior Domain

, Volume 14 (4) – Jul 14, 2017
12 pages

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-017-0966-y
Publisher site
See Article on Publisher Site

### 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} Δ H , p u : = div ( H ( ∇ u ) p - 1 ∇ η H ( ∇ u ) ) where $$1<p<\infty$$ 1 < p < ∞ and $$H:\mathbf {R}^N\rightarrow [0,\infty )$$ H : R N → [ 0 , ∞ ) is in $$C^2(\mathbf {R}^N\backslash \{0\})$$ C 2 ( R N \ { 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 $$1<p\le N$$ 1 < p ≤ N . We also provide an improved version of Hardy inequality for the case $$p=2$$ p = 2 .

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jul 14, 2017

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