Biharmonic Green functions on homogeneous trees
type: Item
instance of: scholarly article
title: Biharmonic Green functions on homogeneous trees
zbMATH Open document ID: 1185.31007
author: Joel M. Cohen
author: Flavia Colonna
author: David Singman
published in: Mediterranean Journal of Mathematics
publication date: 2009-11-18T00:00:00Z
review text: The authors study the simply-supported and the clamped biharmonic Green functions with respect to both Laplacians. The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk \(D\) in \(C\) arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a local placed at another point.
reviewed by: Sophia L. Kalpazidou
Mathematics Subject Classification ID: 31C20
zbMATH DE Number: 5635331
zbMATH Keywords: biharmonic
zbMATH Keywords: trees
zbMATH Keywords: harmonic
MaRDI profile type: Publication
full work available at URL: s00009-009-0014-7
OpenAlex ID: W2034001585
cites work: On the integral representation of superbiharmonic functions
cites work: A NEW BIHARMONIC KERNEL FOR THE UPPER HALF PLANE
cites work: Q4799683
cites work: Solution of biharmonic equations with application to radar imaging
cites work: Integral Geometry on Trees
cites work: Q4769263
cites work: Range of the horocyclic Radon transform on trees
cites work: Q4214026
cites work: Range of the X-ray transform on trees
cites work: The functional analysis of the X-ray transform on trees
cites work: Polyharmonic functions on trees
cites work: A global Riesz decomposition theorem on trees without positive potentials
cites work: Q3559336
cites work: Fractal differential equations on the Sierpiński gasket
cites work: Q3320867
cites work: Tangential limits of potentials on homogeneous trees
cites work: A harmonic calculus on the Sierpinski spaces
cites work: Q3758200
cites work: Q4225028
cites work: A relation between biharmonic Green’s functions of simply supported and clamped bodies
cites work: Q3958740
cites work: Classification theory of Riemannian manifolds. Harmonic, quasiharmonic and biharmonic functions
cites work: Hardy Spaces of Harmonic Functions on Homogeneous Isotropic Trees
DOI: 10.1007/S00009-009-0014-7
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description: scientific article; zbMATH DE number 5635331