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Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions

Published online by Cambridge University Press:  22 January 2016

Ivan J. Singer
Ivan J. Singer*
Affiliation:
University of Miami
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Consider an open Riemann surface R and a density P(z)dxdy (z = x + iy), well defined on R. As was shown by Myrberg in [3], if P ≢ 0 is a nonnegative α-Hölder continuous density on R (0 < α ≤ 1) then there exists the Green’s functions of the differential equation

p>on R, where Δ means the Laplace operator. As a consequence, there always exists a nontrivial solution on R.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 50 , June 1973 , pp. 7 - 20
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

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