Parabolic Harnack, inequality for the heat equation with inverse-square potential

被引：31

作者：

Moschini, Luisa ^{[1
]}

Tesei, Alberto ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy

来源：

FORUM MATHEMATICUM | 2007年 / 19卷 / 03期

关键词：

D O I：

10.1515/FORUM.2007.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A parabolic Harnack inequality for the equation partial derivative(t)u = Delta u + c/vertical bar x vertical bar(2)u (0 < c < co := (n - 2)(2)/4; n >= 3) is proved; in particular, this implies a sharp two-sided estimate for the associated heat kernel. Our approach relies on the unitary equivalence between the Schrodinger operator -Hu=Delta u+ c/x vertical bar(2)u and the weighted Laplacian Delta(lambda)nu=1/vertical bar x vertical bar(lambda)div(vertical bar x vertical bar(lambda)del nu) when lambda = 2-n+ 2 root c(0)-c.

引用

页码：407 / 427

页数：21

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