Zero extension for Poisson’s equation

  • Yongyong Cai
  • Shulin ZhouEmail author


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.


Poisson’s equation zero extension a necessary and sufficient condition 


35J05 31B05 


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Yongyong Cai was supported by National Natural Science Foundation of China (Grant Nos. 91630204 and U1530401). Shulin Zhou was supported by National Natural Science Foundation of China (Grant Nos. 11571020 and 11671021). This work was done when the second author was visiting Beijing Computational Science Research Center (CSRC). The second author thanks CSRC for the hospitality.


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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Beijing Computational Science Research CenterBeijingChina
  2. 2.LMAM and School of Mathematical SciencesPeking UniversityBeijingChina

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