Zero Extension for the Biharmonic Equation
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In this paper we present a necessary and sufficient condition to guarantee that the extended function of the solution by zero extension for the biharmonic equation in a smaller domain is still the solution of the corresponding extension problem in a larger domain. We prove the results under the frameworks of classical solutions and strong solutions.
KeywordsBiharmonic zero extension
MR(2010) Subject Classification35G15 31B30
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This work was done when the second author was visiting Beijing Computational Science Research Center (CSRC). He would like to thank CSRC for the hospitality.
- Chen, Y., Wu, L.: Second order elliptic equations and elliptic systems, translated by Bei Hu, Translations of Mathematical Monographs 174, American Mathematical Society, Providence, RI, 1998Google Scholar
- Evans, L. C.: Partial Differential Equations, Graduate Studies in Mathematics 19, American Mathematical Society, Providence, RI, 1998Google Scholar
- Han, Q.: A Basic Course in Partial Differential Equations, Graduate Studies in Mathematics 120, American Mathematical Society, Providence, RI, 2011Google Scholar
- John, F.: Partial Differential Equations, Fourth Edition, Applied Mathematical Sciences 1, Springer-Verlag, New York, 1981Google Scholar