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A geometrical isoperimetric inequality and applications to problems of mathematical physics

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Commentarii Mathematici Helvetici

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References

  1. Alexandrow, A. D.,Die innere Geometrie der konvexen Flächen, Berlin 1955.

  2. Bandle, C.,Konstruktion isoperimetrischer Ungleichungen der mathematischen Physik aus solchen der Geometrie, Comment. Math. Helv.46 (1971), 182–213.

    MATH  MathSciNet  Google Scholar 

  3. —,Extremaleigenschaften von Kreissektoren und Halbkugeln, Comment. Math. Helv.46 (1971), 356–380.

    MATH  MathSciNet  Google Scholar 

  4. —,Extension d’une inégalité géométrique d’Alexandrow et applications à un problème aux valeurs propres et à un problème de Poisson, C.R. Acad. Sci. Paris277 (1973), 987–989.

    MATH  MathSciNet  Google Scholar 

  5. Bandle, C.,Bounds for the Solutions of Poisson Problems and Applications to Nonlinear Eigenvalue Problems (to appear in SIAM J. Math. Anal.).

  6. Bandle, C.,Isoperimetrische Ungleichungen für den Grundton einer inhomogenen Membran und Anwendungen auf ein nichtlineares Dirichletproblem (to appear in ISNM23).

  7. Behnke, H. andSommer, F.,Theorie der analytischen Funktionen einer komplexen Veränderlichen, Berlin 1955.

  8. Courant, R. andHilbert, D.,Methods of Mathematical Physics, Vol. 1, New York 1965.

  9. Huber, A.,On Subharmonic Functions and Differential Geometry in the Large, Comment. Math Helv.32 (1957), 13–72.

    Article  MATH  MathSciNet  Google Scholar 

  10. —,Zum potentialtheoretischen Aspekt der Alexandrowschen Flächentheorie, Comment. Math. Helv.34 (1960), 99–126.

    Article  MATH  MathSciNet  Google Scholar 

  11. Nehari, Z.,On the Principal Frequency of a Membrane, Pac. J. Math.8 (1958), 285–293.

    MATH  MathSciNet  Google Scholar 

  12. Pólya, G. andSzegö, G.,Isoperimetric Inequalities in Mathematical Physics, Princeton (1951).

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Bandle, C. A geometrical isoperimetric inequality and applications to problems of mathematical physics. Commentarii Mathematici Helvetici 49, 496–511 (1974). https://doi.org/10.1007/BF02566745

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