Abstract This paper is the second installment in a series of papers concerning the boundary behavior of solutions to the p-parabolic equations. In this paper we are interested in the short time behavior of the solutions, which is in contrast with much of the literature, where all results require a waiting time. We prove a dichotomy about the decay-rate of non-negative solutions vanishing on the lateral boundary in a cylindrical C 1 , 1 domain. Furthermore we connect this dichotomy to the support of the boundary type Riesz measure related to the p-parabolic equation in NTA-domains, which has consequences for the continuation of solutions.

中文翻译：

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抛物线 p-拉普拉斯方程 II 解的边界行为

摘要 本文是关于 p 抛物线方程解的边界行为系列论文的第二部分。在本文中，我们对解决方案的短时间行为感兴趣，这与许多文献形成对比，其中所有结果都需要等待时间。我们证明了关于在圆柱形 C 1, 1 域中的横向边界上消失的非负解的衰减率的二分法。此外，我们将这种二分法与与 NTA 域中 p 抛物线方程相关的边界类型 Riesz 测度的支持联系起来，这对解的延续有影响。