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.
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页码：131 / 183
页数：53
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