Some evaluations of the fractional p-Laplace operator on radial functions
We face a rigidity problem for the fractional $ p $-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that $ (-\Delta)^s(1-|x|^{2})^s_+ $ and $ -\Delta_p(1-|x|^{\frac{p}{p-1}}) $ are constant functions in $ (-1, 1) $ for fixed $ p $ and $ s $. We eva...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-02-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023015?viewType=HTML |
| Summary: | We face a rigidity problem for the fractional $ p $-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that $ (-\Delta)^s(1-|x|^{2})^s_+ $ and $ -\Delta_p(1-|x|^{\frac{p}{p-1}}) $ are constant functions in $ (-1, 1) $ for fixed $ p $ and $ s $. We evaluated $ (-\Delta_p)^s(1-|x|^{\frac{p}{p-1}})^s_+ $ proving that it is not constant in $ (-1, 1) $ for some $ p\in (1, +\infty) $ and $ s\in (0, 1) $. This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas. |
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| ISSN: | 2640-3501 |