Wiener's criterion for the heat equation
Wiener's criterion for the heat equation
复制标题
热方程的维纳准则
DOI：
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
Ronald F. Gariepy
中科院分区：
文献类型：
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作者：
Lawrence C. Evans;Ronald F. Gariepy
本文建立了热方程R“+1的任意有界开子集的边界点正则的充要条件。我们的标准是，在下面描述的意义上，确切的模拟赢家的测试[W]的边界正则性的调和函数。要仔细说明我们的结果，首先需要引入大量的术语。Let .（2 QR“+1（n ~ 1））表示任意有界开子集，8/2表示它的拓扑边界.我们经常将典型点z E R“+1写成z =（x，t），xER~，tE R。如果uE C2（-Q;R），我们可以定义热算子
This paper establishes a necessary and sufficient condition for a boundary point of an arbitrary bounded open subset of R "+1 to be regular for the heat equation. Our criterion is, in the sense described below, the exact analogue of WINNER'S test [W] for boundary regularity of harmonic functions. A careful statement of our result requires that we first of all introduce a great deal of terminology. Let .(2 Q R "+1 (n ~ 1) denote any bounded open subset and 8/2 its topological boundary. We will often write a typical point z E R "+1 as z = (x, t), xER~, tE R. If uE C2(-Q;R) we may define the heat operator