The fractional Hardy inequality with a remainder term

Details The fractional Hardy inequality with a remainder term The fractional Hardy inequality with a remainder term

2009-07-25

arxiv.org/abs/0907.4448v2

Colloq. Math. 122 (2011), 59-67

Mathematics

Analysis of PDEs

Major changes

Scientific paper

10.4064/cm122-1-6

We calculate the regional fractional Laplacian on some power function on an interval. As an application, we prove Hardy inequality with an extra term for the fractional Laplacian on the interval with the optimal constant. As a result, we obtain the fractional Hardy inequality with best constant and an extra lower-order term for general domains, following the method developed by M. Loss and C. Sloane [arXiv:0907.3054v1 [math.AP]]

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