Optimal Hardy inequalities in cones

被引：16
|
作者：
Devyver, Baptiste [1 ]
Pinchover, Yehuda [2 ]
Psaradakis, Georgios [2 ]
机构：
[1] Univ British Columbia, Dept Math, Vancouver, BC V6T IZ2, Canada
[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2017年 / 147卷 / 01期
基金：
以色列科学基金会; 加拿大自然科学与工程研究理事会;
关键词：
Hardy inequality; minimal growth; positive solutions; POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; OPERATORS;
D O I：
10.1017/S0308210516000056
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Omega be an open connected cone in R-n with vertex at the origin. Assume that the operator P mu := -Delta - mu/delta(2)(Omega) (x) is subcritical in Omega, where delta(Omega) is the distance function to the boundary of Omega and mu <= 1/ 4. We show that under some smoothness assumption on Omega the improved Hardy-type inequality integral(Omega)vertical bar del phi vertical bar(2) dx - mu integral(Omega) vertical bar phi vertical bar(2) /delta(2)(Omega) dx >= lambda(mu) integral(Omega) vertical bar phi vertical bar(2) /vertical bar x vertical bar(2) dx for all phi epsilon C-0(infinity) (Omega) holds true, and the Hardy-weight lambda( mu)vertical bar x vertical bar(-2) is optimal in a certain definite sense. The constant lambda(mu) > 0 is given explicitly.
引用
收藏
页码：89 / 124
页数：36
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