Zero extension for Poisson's equation

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 721-732
• 页数: 12页
• 语种: 英文

摘要

In this paper,we present a necessary and sufficient condition to guarantee that the extended function of the solution for Poisson's equation in a smaller domain by zero extension is still the solution of the corresponding extension problem in a larger domain.We prove the results under the frameworks of classical solutions,strong solutions and weak solutions.Furthermore,we give some observations for the nonlinear p-Laplace equation.