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The Dirichlet Problem on Ends

In: Potential Theory

Author

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  • Teruo Ikegami

    (Osaka City University, Department of Mathematics)

Abstract

In the recent investigations of the Dirichlet problem in an axiomatic framework we focus our interest on the following two problems: (1) the boundary behavior of the normalized PWB-solutions, originally studied by O. Frostman[3] and generalized by Constantinescu-Cornea[2] and Lukeš-Malý[11] and (2) the unicity of Keldych operators formulated by J. Lukeš[10], given by Bliedtner-Hansen[1] its essential contribution. The normalized PWB-solutions H f U,X on an open set U is formed by the Perron-Wiener-Brelot’s method taking the closure of U in the one-point compactified space and putting f to be 0 at the infinity, and the effect of the ideal boundary is neglected. In this article we consider above problem under the full influence of the ideal boundary and in the conclusing result we reflect that our result is a generalized version of that obtained formerly.

Suggested Citation

  • Teruo Ikegami, 1988. "The Dirichlet Problem on Ends," Springer Books, in: Josef Král & Jaroslav Lukeš & Ivan Netuka & Jiří Veselý (ed.), Potential Theory, pages 131-136, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0981-9_17
    DOI: 10.1007/978-1-4613-0981-9_17
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