Capacitary estimates of solutions of semilinear parabolic equations

被引：6

作者：

Marcus, Moshe ^{[1
]}

Veron, Laurent ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[2] Univ Tours, Dept Math, Tours, France

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2013年 / 48卷 / 1-2期

基金：

以色列科学基金会;

关键词：

POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; BOUNDARY TRACE; SINGULARITIES;

D O I：

10.1007/s00526-012-0545-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that any positive solution of in with initial trace (F, 0), where F is a closed subset of can be represented, up to two universal multiplicative constants, by a series involving the Bessel capacity . As a consequence we prove that there exists a unique positive solution of the equation with such an initial trace. We also characterize the blow-up set of u(x, t) when , by using the "density" of F expressed in terms of the -Bessel capacity.

引用

页码：131 / 183

页数：53

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