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 corre...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 pLaplace equation.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.91630204 and U1530401)supported by National Natural Science Foundation of China(Grant Nos.11571020 and 11671021)。
文摘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 pLaplace equation.