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On the behavior of a non-parametric minimal surface in a non-convex quadrilateral

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References

  1. Beeson, Michael, “The behavior of a minimal surface in a corner”, Arch. Rational Mech. Anal. 65 (4) 1977, 379–393.

    Google Scholar 

  2. Concus, Paul, “Numerical study of the discrete minimal surface equation in a nonconvex domain”, Lawrence Berkeley Laboratory TID-4500–R60, June 1973.

  3. Federer, Herbert, Geometric Measure Theory, Springer-Verlag, Berlin Heidelberg New York, 1969.

    Google Scholar 

  4. Finn, Robert, “Remarks relevant to minimal surfaces, and to surfaces of prescribed mean curvature”, J. d'Anal. Math. 14 (1965), 139–160.

    Google Scholar 

  5. Finn, Robert, “New estimates for equations of minimal surface type”, Arch. Rational Mech. Anal. 14 (1963), 337–375.

    Google Scholar 

  6. Gerhardt, Claus, “Existence, regularity, and boundary behavior of generalized surfaces of prescribed mean curvature”, Math. Z. 139 (1974), 173–198.

    Google Scholar 

  7. Gerhardt, Claus, “On the regularity of solutions to variational problems in BV(Ω)”, Math. Z. 149 (1976), 281–286.

    Google Scholar 

  8. Gagliardo, Emilio, “Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili”, Rend. Sem. Mat. Univ. Padova 27 (1957), 284–305.

    Google Scholar 

  9. Giusti, Enrico, Minimal Surfaces and Functions of Bounded Variation, Notes on Pure Mathematics 10, Department of Mathematics, Australian National University, 1977.

  10. Giusti, Enrico, “Superfici Cartesiane di area minima”, Rend, del Sem. Mat. Milano (1970), 3–21.

  11. Gilbarg, David & Trudinger, Neil, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin Heidelberg New York 1977.

    Google Scholar 

  12. Jenkins, Howard & Serrin, James, “Variational problems of minimal surface type II. Boundary value problems for the minimal surface equation”, Arch. Rational Mech. Anal. 21 (1966), 321–342.

    Google Scholar 

  13. Lancaster, Kirk, “Boundary behavior of a non-parametric minimal surface in IR3 at a non-convex point”, Analysis 5 (1985) 61–69.

    Google Scholar 

  14. Meyers, Norman & Ziemer, William, “Integral inequalities of Poincaré and Wirtinger type for BV functions”, Amer. J. Math. 99 (6) (1977), 1345–1360.

    Google Scholar 

  15. Nitsche, J. C. C., “On the nonsolvability of Dirichlet's problem for the minimal surface equation”, J. Math. Mech. 14 (1965), 779–788.

    Google Scholar 

  16. Nitsche, J. C. C., “On new results in the theory of minimal surfaces”, Bull. Amer. Math. Soc. 71 (1965), 195–270.

    Google Scholar 

  17. Nitsche, J. C. C., “Über ein verallgemeinertes Dirichletsches Problem für die Minimalflächengleichung und hebbare Unstetigkeiten ihrer Lösungen”, Math. Ann. 158 (1965), 203–214.

    Google Scholar 

  18. Nitsche, J. C. C., Vorlesungen über Minimalflächen, Springer-Verlag, Berlin Heidelberg New York 1975.

    Google Scholar 

  19. Osserman, Robert, A Survey of Minimal Surfaces, Van Nostrand, 1969.

  20. Rado, Tibor, “Contributions to the theory of minimal surfaces”, Acta. Litt. Scient. Univ. Szeged 6 (1932), 1–20.

    Google Scholar 

  21. Serrin, James, “A priori estimates for solutions of the minimal surface equation”, Arch. Rational Mech. Anal. 14 (1963), 376–383.

    Google Scholar 

  22. Trudinger, Neil, “On the analyticity of generalized minimal surfaces”, Bull. Austral. Math. Soc. 5 (1971), 315–320.

    Google Scholar 

  23. Williams, Graham, “Surfaces of prescribed mean curvature with inequalities on the boundary”, Math. Z 164 (1978), 31–51.

    Google Scholar 

  24. Williams, Graham, “The equivalence of some variational problems for surfaces of prescribed mean curvature”, Bull. Austral. Math. Soc. 20 (1979), 87–104.

    Google Scholar 

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Communicated by J. C. C. Nitsche

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Elcrat, A.R., Lancaster, K.E. On the behavior of a non-parametric minimal surface in a non-convex quadrilateral. Arch. Rational Mech. Anal. 94, 209–226 (1986). https://doi.org/10.1007/BF00279863

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