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Some extremal problems for functions of bounded boundary rotation

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Abstract

A variational method is developed within the class of functions of boundary rotation not exceedingkπ which is based on the fact that the set of representing measuresμ is convex. It shows that an extremal problem related to a functional with Gâteaux derivative and some constraints leads to extremal measuresμ 0 with finite support. The positive and negative part of aμ 0 is located at points where a functionJ (depending onμ 0) reaches its maximum and minimum respectively. The method is tested successfully on various problems.

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Authors and Affiliations

  1. Imperial College, London, England

    Roman Boutellier & Albert Pfluger

  2. Eidg. Techn. Hochschule, CH-8092, Zurich, Switzerland

    Roman Boutellier & Albert Pfluger

Authors
  1. Roman Boutellier
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  2. Albert Pfluger
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Boutellier, R., Pfluger, A. Some extremal problems for functions of bounded boundary rotation. Israel J. Math. 39, 46–62 (1981). https://doi.org/10.1007/BF02762852

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  • DOI: https://doi.org/10.1007/BF02762852

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