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- W2034001585 abstract "The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk $${mathbb{D}}$$ in $${mathbb{C}}$$ 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 load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of the unit disk endowed with the Poincare metric. The usual Laplace operator on T corresponds to the hyperbolic Laplacian. In this work, we consider a bounded metric on T for which T is relatively compact and use it to define a flat Laplacian which plays the same role as the ordinary Laplace operator on $${mathbb{D}}$$ . We then study the simply-supported and the clamped biharmonic Green functions with respect to both Laplacians." @default.
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- W2034001585 date "2009-09-10" @default.
- W2034001585 modified "2023-09-26" @default.
- W2034001585 title "Biharmonic Green Functions on Homogeneous Trees" @default.
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- W2034001585 doi "https://doi.org/10.1007/s00009-009-0014-7" @default.
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