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Funktionenfamilien mit einem Maximumprinzip und elliptische Differentialgleichungen II

Families of functions with a maximum principle and elliptic differential equations II

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Abstract

The present paper deals with the application of the theory developed in part I to some elliptic differential equations. Representations of solutions of this differential equations are given by generalized power series and by Bergman integral operators respectively. For in an annulus bounded solutions a generalisation of the three circle theorem due to Hadamard is derived in two different manners. The application of theorems of part I gives the first case and the second one uses the aid of a fundamental system of solutions of an associated ordinary differential equation. This fundamental system is also represented by an integral operator of Bergman type.

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Literatur

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Authors and Affiliations

  1. I. Lehrkanzel für Mathematik, Technische Hochschule Graz, Kopernikusgasse 24, A-8010, Graz, Österreich

    Gerhard Jank

  2. Mathematisches Institut der Universität Bonn, Wegelerstraße 10, D-5300, Bonn, Bundesrepublik Deutschland

    Stephan Ruscheweyh

Authors
  1. Gerhard Jank
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  2. Stephan Ruscheweyh
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Jank, G., Ruscheweyh, S. Funktionenfamilien mit einem Maximumprinzip und elliptische Differentialgleichungen II. Monatshefte fü Mathematik 79, 103–113 (1975). https://doi.org/10.1007/BF01585666

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  • DOI: https://doi.org/10.1007/BF01585666

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