Fractional calculus for power functions and eigenvalues of the fractional Laplacian

被引：0
作者：
Bartłlomiej Dyda
机构：
[1] University of Bielefeld,Faculty of Mathematics
[2] Wrocław University of Technology,Institute of Mathematics and Computer Science
来源：
Fractional Calculus and Applied Analysis | 2012年 / 15卷
关键词：
fractional Laplacian; ball; killed stable process; eigenvalue; power function; hypergeometric function; Primary 35P15; Secondary 60G52, 31C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We calculate the fractional Laplacian Δα/2 for functions of the form u(x) = (1 − |x|2)+p and v(x) = xdu(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.
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页码：536 / 555
页数：19
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