Sharp Estimates for Derivatives of Functions in the Sobolev Classes (W)over-circle2r(-1,1)

被引：0

作者：

Kalyabin, G. A. ^{[1
]}

机构：

[1] Peoples Friendship Univ Russia, Moscow 117198, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2010年 / 269卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

D O I：

10.1134/S0081543810020112

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Explicit formulas are obtained for the maximum possible values of the derivatives f((k))(x), x epsilon (-1, 1), kappa epsilon {0, 1, ... , r - 1}, for functions f that vanish together with their (absolutely continuous) derivatives of order up to <= r - 1 at the points +/- 1 and are such that parallel to f((r))parallel to(L2(- 1, 1)) <= 1. As a corollary, it is shown that the first eigenvalue lambda(1,r) of the operator (-D-2)(r) with these boundary conditions is root 2(2r)! (1+O(1/r)), r -> infinity.

引用

页码：137 / 142

页数：6

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