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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A relation between two biharmonic Green's functions on Riemannian manifolds


Author: Dennis Hada
Journal: Trans. Amer. Math. Soc. 227 (1977), 251-261
MSC: Primary 31C10
DOI: https://doi.org/10.1090/S0002-9947-1977-0430283-5
MathSciNet review: 0430283
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Abstract: The biharmonic Green's function $ \gamma $ whose values and Laplacian are identically zero on the boundary of a region and the biharmonic Green's function $ \Gamma $ whose values and normal derivative vanish on the boundary originated in the investigation of thin plates whose edges are simply supported or clamped, respectively. A relation between these two biharmonic Green's functions known for planar regions is extended to Riemannian manifolds thereby establishing that any Riemannian manifold for which $ \gamma $ exists must also carry $ \Gamma $.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0430283-5
Keywords: Biharmonic Green's functions, biharmonic reproducing kernel, Riemannian manifold
Article copyright: © Copyright 1977 American Mathematical Society