On semilinear elliptic equations with borderline Hardy potentials

被引：14

作者：

Felli, Veronica ^{[1
]}

Ferrero, Alberto ^{[2
]}

机构：

[1] Univ Milano Bicocca, I-20125 Milan, Italy

[2] Univ Piemonte Orientale, I-15121 Alessandria, Italy

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2014年 / 123卷

关键词：

SCHRODINGER-EQUATIONS; ASYMPTOTIC-BEHAVIOR; EXISTENCE; WEIGHTS;

D O I：

10.1007/s11854-014-0022-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the asymptotic behavior of solutions of an elliptic equation near the singularity of an inverse square potential with a coefficient related to the best constant for the Hardy inequality. Due to the presence of a borderline Hardy potential, a proper variational setting has to be introduced in order to provide a weak formulation of the equation. An Almgren-type monotonicity formula is used to determine the exact asymptotic behavior of solutions.

引用

页码：303 / 340

页数：38

共 32 条

[1] An improved Hardy-Sobolev inequality and its application [J].