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Mean value theorems for functions satisfying the inequality Δu+Keu≧0

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References

  1. Ahlfors, S., Geodesic curvature and area, Studies in Mathematical Analysis and Related Topics: Essays in honor of G. Pólya, Stanford University Press, California 1962, 1–7.

    Google Scholar 

  2. Bandle, C., Extensions of an inequality by Pólya and Schiffer. Pac. J. Math. 42, 543–555 (1972).

    Google Scholar 

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

    Google Scholar 

  4. Bellman, R., On the non-negativity of Green's functions. Boll. Unione Matem. Ital. 12, 411–413 (1957).

    Google Scholar 

  5. Bol, G., Isoperimetrische Ungleichung für Bereiche auf Flächen. Jahresbericht d. Deutschen Mathem.-Vereinigung 51, 219–257 (1941).

    Google Scholar 

  6. Cohen, D. S., & H. B. Keller, Some positone problems suggested by nonlinear heat generation. J. Math. Mech. 16, 1361–1376 (1967).

    Google Scholar 

  7. Courant, R., & D. Hilbert, Methods of Mathematical Physics, vol. 2. New York: Interscience 1962.

    Google Scholar 

  8. Fiala, F., Le problème des isopérimètres sur les surfaces ouvertes à courbure positive. Comment. Math. Helv. 13, 293–346 (1940–41).

    Google Scholar 

  9. Fujita, H., On the nonlinear equations \(\Delta u + e^u = {\text{0}}\frac{{\partial v}}{{\partial t}} = \Delta v{\text{ + }}e^v \). Bull. Amer. Math. Soc. 75, 132–135 (1969).

    Google Scholar 

  10. Gelfand, J. M., Some problems in the theory of quasilinear equations. Amer. Math. Soc. Transl. Ser. 2, 29, 295–381 (1963).

    Google Scholar 

  11. Hartman, P., Geodesic parallel coordinates in the large. Amer. J. of Math. 86, 705–727 (1964).

    Google Scholar 

  12. Osserman, R., On the inequality Δu≦f(u). Pac. J. Math. 7, 1641–1647 (1957).

    Google Scholar 

  13. Pólya, G., & M. Schiffer, Convexity of functional by transplantation. J. Anal. Math. 3, 245–345 (1953–54).

    Google Scholar 

  14. Pólya, G., & G. Szegö, Aufgaben und Lehrsätze aus der Analysis, vol. 2. Berlin: Springer 1925.

    Google Scholar 

  15. Pólya, G., & G. Szegö, Isoperimetric Inequalities in Mathematical Physics. Princeton: Van Nostrand 1951.

    Google Scholar 

  16. Saks, The Theory of Integral. New York: Hafner.

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Authors and Affiliations

  1. Eidgenössische Technische Hochschule Zürich Forschungsinstitut für Mathematik, Germany

    Catherine Bandle

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  1. Catherine Bandle
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Communicated by M. M. Schiffer

The author wishes to thank Professor M. M. Schiffer for his encouragement and help during the preparation of this paper.

This work was supported by the Swiss National Foundation of Science.

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Bandle, C. Mean value theorems for functions satisfying the inequality Δu+Keu≧0. Arch. Rational Mech. Anal. 51, 70–84 (1973). https://doi.org/10.1007/BF00275994

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  • DOI: https://doi.org/10.1007/BF00275994

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