Poisson方程在边界附近的零延拓

Zero extension for Poisson equation near the boundary

本文给出一个充分必要条件,来保证Poisson方程的解在边界附近零延拓后得到的函数仍然是相对应的延拓问题的解.本文分别在古典解、强解和弱解的框架下证明这个结果.

In this paper we present a necessary and sufficient condition to guarantee that the extended function of the solution for Poisson equation by zero extension near the boundary of a domain is still the solution of the corresponding extension problem in the extended domain. We prove the results under the frameworks of classical solutions, strong solutions and weak solutions.