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Variational problems of minimal surface type. I

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References

  1. Bers, L., & L. Nirenberg: On linear and non-linear elliptic boundary value problems in the plane. Atti del Convegno Internazionale sulle Equazioni alle Derivate Parziali (Trieste), 141–167. Rome, 1955.

  2. Birkhoff, G., & G.-C. Rota: Ordinary Differential Equations. New York 1961.

  3. Finn, R.: Isolated singularities of solutions of nonlinear partial differential equations. Trans. Amer. Math. Soc. 75, 385–404 (1953).

    Article  MATH  MathSciNet  Google Scholar 

  4. Finn, R.: On equations of minimal surface type. Ann. of Math. 60, 397–416 (1954).

    Article  MATH  MathSciNet  Google Scholar 

  5. Finn, R., & J. Serrin: On the Hölder continuity of quasi-conformal and elliptic mappings. Trans. Amer. Math. Soc. 89, 1–15 (1958).

    Article  MATH  MathSciNet  Google Scholar 

  6. Heinz, E.: Über die Lösungen der Minimalflächengleichung. Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. 1952, 51–56.

  7. Hopf, E.: On an inequality for minimal surfaces z = ϕ(x, y). J. Rational Mech. Analysis 2, 519–522 (1953).

    MATH  MathSciNet  Google Scholar 

  8. Jenkins, H.: On quasi-linear elliptic equations which arise from variational problems. J. Math. Mech. 10, 705–727 (1961).

    MATH  MathSciNet  Google Scholar 

  9. Jenkins, H.: On two-dimensional variational problems in parametric form. Arch. Rational Mech. Analysis 8, 181–206 (1961).

    MATH  MathSciNet  ADS  Google Scholar 

  10. Meyers, N.: On a class of nonuniformly elliptic quasi-linear equations in the plane. To appear in this journal.

  11. Nitsche, J. C. C.: On an estimate for the curvature of minimal surfaces z = ϕ(x,y). J. Math. Mech. 7, 767–770 (1958).

    MATH  MathSciNet  Google Scholar 

  12. Osserman, R.: On the Gauss curvature of minimal surfaces. Trans. Amer. Math. Soc. 96, 115–128 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  13. Serrin, J.: On the Harnack inequality for linear elliptic equations. J. d'Analyse Mathématique 4, 292–308 (1956).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Technology University of Minnesota, Minneapolis, Minnesota

    Howard Jenkins & James Serrin

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  1. Howard Jenkins
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  2. James Serrin
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Note. This work was partially supported by the United States Air Force Office of Scientific Research and Development under Grant No. AF-AFOSR-62-101.

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Jenkins, H., Serrin, J. Variational problems of minimal surface type. I. Arch. Rational Mech. Anal. 12, 185–212 (1963). https://doi.org/10.1007/BF00281225

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