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Mathematics
Volume 13
Issue 11
10.3390/math13111774
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Zero Extension for the Dirichlet Problem of the Biharmonic Equation

by
Shaopeng Xu
1,2,* and
Chong Yu
3
1
School of Mathematics and Statistics, Hainan University, Haikou 570228, China
2
Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Hainan University, Haikou 570228, China
3
International Business School, Hainan University,Haikou 570228, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1774; https://doi.org/10.3390/math13111774
Submission received: 24 April 2025 / Revised: 20 May 2025 / Accepted: 23 May 2025 / Published: 26 May 2025
Versions Notes

Abstract

In this paper, we consider whether the zero extension of a solution to the Dirichlet problem for the biharmonic equation in a smaller domain remains a solution to the corresponding extended problem in a larger domain. We analyze classical and strong solutions, and present a necessary and sufficient condition under each framework, respectively.
Keywords: biharmonic; dirichlet problem; zero extension biharmonic; dirichlet problem; zero extension

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MDPI and ACS Style

Xu, S.; Yu, C. Zero Extension for the Dirichlet Problem of the Biharmonic Equation. Mathematics 2025, 13, 1774. https://doi.org/10.3390/math13111774

AMA Style

Xu S, Yu C. Zero Extension for the Dirichlet Problem of the Biharmonic Equation. Mathematics. 2025; 13(11):1774. https://doi.org/10.3390/math13111774

Chicago/Turabian Style

Xu, Shaopeng, and Chong Yu. 2025. "Zero Extension for the Dirichlet Problem of the Biharmonic Equation" Mathematics 13, no. 11: 1774. https://doi.org/10.3390/math13111774

APA Style

Xu, S., & Yu, C. (2025). Zero Extension for the Dirichlet Problem of the Biharmonic Equation. Mathematics, 13(11), 1774. https://doi.org/10.3390/math13111774

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