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The calculus of variations today

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Bibliography

  1. F. Almgren, Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints.Memoirs of the Amer. Math. Soc. 4, No. 165 (1976).

    Google Scholar 

  2. J. M. Ball, editor,Systems of nonlinear partial differential equations. NATO ASI series, Series C, No. 111, Proc. of NATO Adv. Study Inst. Oxford 1982, Reidel Publ., Dordrecht-Boston-Lancaster (1983).

    MATH  Google Scholar 

  3. M. Giaquinta,Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Math. Studies, Princeton Univ. Press (1983).

  4. D. Gilbarg and N. Trudinger,Elliptic partial differential equations of second order, Heidelberg-New York: Springer- Verlag (1977).

    Book  MATH  Google Scholar 

  5. D. Hilbert, Mathematische Probleme,Archiv f. Math. und Phys. 3. Reihe, Bd. 1, 44–63, 213-237 (1901), und: Ges.Abhandl. Bd. 3, Springer-Verlag, 290-329 (1935).

    MATH  Google Scholar 

  6. S. Hildebrandt, Nonlinear elliptic systems and harmonic mappings,Proc. 1980 Beijing Symp. on Diff. Geom. and Diff. Equ., Vol. 1, Beijing: Science Press (1982) 481–615.

    Google Scholar 

  7. S. Hildebrandt, Calculus of Variations Today, reflected in the Oberwolfach meetings,Perspectives in mathematics, W. Jäger, J. Moser, R. Remmert, (ed.), Basel-Boston-Stuttgart: Birkhäuser Verlag (1983), 321–336.

    Google Scholar 

  8. S. Hildebrandt and A. Tromba,Mathematics and Optimal Form, Scientif. Amer. Library, New York: W. H. Freeman and Co. (1985).

    Google Scholar 

  9. O. A. Ladyzenskaja and N. N. Uralzeva,Linear and quasilinear elliptic equations, New York and London: Acad. Press (1968).

    Google Scholar 

  10. C. B. Morrey,Multiple integrals in the calculus of variations, Berlin-Heidelberg-New York: Springer-Verlag (1966).

    MATH  Google Scholar 

  11. J. C. C. Nitsche,Vorlesungen über Minimalflächen, Berlin- Heidelberg-New York: Springer-Verlag (1975).

    Book  MATH  Google Scholar 

  12. L. Simon,Lectures on Geometric Measure Theory, Centre for Math. Anal., Austral. Nat. Univ. Canberra Vol. 3 (1983).

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  • Figures 1, 6, 10: S. Hildebrandt and A. Tromba,Mathematics and Optimal Form, New York: W. H. Freeman & Co. (1985).

    Google Scholar 

  • Figure 2: S. Hildebrandt and J. C. C. Nitsche, A uniqueness theorem for surfaces of least area with partially free boundaries on obstacles,Archive for Rational Mechanics and Analysis 79, 189–218 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  • Figures 3, 5, 8, 9: Bildarchiv. Inst. für Leichte Flächentragwerke, Universität Stuttgart.

  • Figure 7: E. Häckel,Reports of the Scientific Results of H.M.S. Challenger, London, 1881–89.

  • Figure 14: B. Winkel und J. Krön,Minimalwegenetze mit vielen Knoten, Studienarbeit 2/1985, Inst. für Leichte Flächentragwerke, TU Stuttgart.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, D-5300, Bonn, Federal Republic of Germany

    Stefan Hildebrandt

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  1. Stefan Hildebrandt
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Additional information

This article is an edited translation ofVariationsrechnung heute, which was published by the Rheinisch-Westfälische Akademie der Wissenschaften inNatur-, Ingenieur- und Wirtschaftswissenschaßen 345 (1986). The original paper in German was based upon a lecture intended for non-mathematicians.

The translator wishes to thank the author and his friends George Booth and Hardy Grant for reading the translation and suggesting a number of improvements.

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Hildebrandt, S. The calculus of variations today. The Mathematical Intelligencer 11, 50–60 (1989). https://doi.org/10.1007/BF03025887

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