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Dirichlet finite biharmonic functions on the plane with distorted metrics

Published online by Cambridge University Press:  22 January 2016

Mitsuru Nakai
Mitsuru Nakai*
Affiliation:
Nagoya University
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The Laplace-Beltrami operator Δ on a smooth manifold M with a smooth Riemannian metric ds2 = ∑i,jgij(x)dxidxj applied to a smooth function φ takes the form Functions in the class H2(M) = {u∈ C4(M); Δ2u = 0} are called biharmonic.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 51 , September 1973 , pp. 131 - 135
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Sario, M. Nakai-L.: Existence of Dirichlet finite biharmonic functions, Ann. Acad. Sci. Fenn., 532 (1973), 1–34.Google Scholar
[2] O’Malla, H.: Dirichlet finite biharmonic functions on the unit disk with distorted metrics, Proc. Amer. Math. Soc., 32 (1972), 521–524.Google Scholar
[3] Nakai, L. Sario-M.: Classification Theory of Riemann Surfaces, Springer, 1970.Google Scholar