Solutions to the prescribed mean curvature equation
DOI:
https://doi.org/10.22199/S07160917.1999.0002.00003Abstract
We apply variational methods in order to prove that the nonlinear system (1) admits at least one regular solution.
References
[1] Amster P. Mariani, M. C., Rial, D. F. : Existence and uniqueness of H-System's solutions with Dirichlet conditions. To appear in Nonlinear Analysis, Theory, Methods, and Applications.
[2] Bethuel, F. : Un résultat de regularité pour les solutions de l'equation des surfaces à courboure moyenne prescrite. R. Acad. Sci. Paris Sér. I Math 314, n° 13, pp. 1003- 100, (1992).
[3] Brezis, H., Coron, J., Multiple Solutions of H-Systems and Rellich's conjecture. Comm. Pure Appl. Math 37, pp. 149- 187, (1984).
[4] Chanillo S. , Li Y. : Continuity of Solutions of Uniformly Elliptic Equations in R2 . Manuscripta math. 77, pp. 415-433, (1992).
[5] Gilbarg, D., Trudinger N. : Elliptic Partial Differential Equations of Second Order. Springer-Verlag (1977).
[6] Osserman, R. : A Survey of Minimal Surfaces. Van Nostrand Reinhold Company, ( 1969).
[7] Struwe, M.: Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, pp. 180.
[8] Wente, H. : An Existence Theorem for Surfaces of Constant Mean Curvature. Journal of Mathematical Analysis and Applications 26, pp. 318-344, (1969)
[9] Wente, H. : The differential equation ?X = 2H(Xu ? Xv) with vanishing boundary values. Proceedings of the American Mathematical Society 50, pp.131-7, (1975).
[2] Bethuel, F. : Un résultat de regularité pour les solutions de l'equation des surfaces à courboure moyenne prescrite. R. Acad. Sci. Paris Sér. I Math 314, n° 13, pp. 1003- 100, (1992).
[3] Brezis, H., Coron, J., Multiple Solutions of H-Systems and Rellich's conjecture. Comm. Pure Appl. Math 37, pp. 149- 187, (1984).
[4] Chanillo S. , Li Y. : Continuity of Solutions of Uniformly Elliptic Equations in R2 . Manuscripta math. 77, pp. 415-433, (1992).
[5] Gilbarg, D., Trudinger N. : Elliptic Partial Differential Equations of Second Order. Springer-Verlag (1977).
[6] Osserman, R. : A Survey of Minimal Surfaces. Van Nostrand Reinhold Company, ( 1969).
[7] Struwe, M.: Variational Methods, Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, pp. 180.
[8] Wente, H. : An Existence Theorem for Surfaces of Constant Mean Curvature. Journal of Mathematical Analysis and Applications 26, pp. 318-344, (1969)
[9] Wente, H. : The differential equation ?X = 2H(Xu ? Xv) with vanishing boundary values. Proceedings of the American Mathematical Society 50, pp.131-7, (1975).
Published
2018-04-04
How to Cite
[1]
P. Amster, P. De Nápoli, and M. C. Mariani, “Solutions to the prescribed mean curvature equation”, Proyecciones (Antofagasta, On line), vol. 18, no. 2, pp. 155-164, Apr. 2018.
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