On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 2, pp. 191-214. 
@article{AIHPC_1993__10_2_191_0,
     author = {Duzaar, Frank},
     title = {On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {191--214},
     publisher = {Gauthier-Villars},
     volume = {10},
     number = {2},
     year = {1993},
     mrnumber = {1220033},
     zbl = {0808.49036},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1993__10_2_191_0/}
}
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Duzaar, Frank. On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 2, pp. 191-214. http://archive.numdam.org/item/AIHPC_1993__10_2_191_0/

[AW] W.K. Allard, On the first variation of a varifold, Ann. of Math., Vol. 95, 1972, pp. 417-491. | MR | Zbl

[DF1] F. Duzaar and M. Fuchs, Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmung, Zeitschrift für Analysis und ihre Anwendungen, Vol. 10, 4, 1991, pp. 525-534. | MR | Zbl

[DF2 F. Duzaar and M. Fuchs, On the existence of integral currents with prescribed mean curvature vector, Manus. math., Vol. 67, 1990, pp. 41-67. | MR | Zbl

[DF3] F. Duzaar and M. Fuchs, On integral currents with constant mean curvature, Rend. Sem. Mat. Univ. Padova, Vol. 85, 1991, pp. 79-103. | Numdam | MR | Zbl

[DF4] F. Duzaar and M. Fuchs, A general existence theorem for integral currents with prescribed mean curvature form, in Boll. U.M.I., 1992 (to appear). | MR | Zbl

[Fe] H. Federer, Geometric measure theory, Springer, Berlin, Heidelberg, New York, 1969. | MR | Zbl

[Fe1] H. Federger, The singular set of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc., Vol. 76, 1970, pp. 767-771. | MR | Zbl

[GS1] R. Gulliver and J. Spruck, Existence theorems for parametric surfaces of prescribed mean curvature, Indiana Univ. Math. J., Vol. 22, 1972, pp. 258-287. | MR | Zbl

[GS2] R. Gulliver and J. Spruck, The Plateau problem for surfaces of prescribed mean curvature in a cylinder, Invent. Math., Vol. 13, 1971, pp. 169-178. | MR | Zbl

[GT] D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, second Ed., Springer, Berlin, Heidelberg, New York, 1977. | MR | Zbl

[Hi] S. Hildebrandt, Randwertprobleme für Flächen vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapilaritätstheorie. I. Math. Z., Vol. 115, 1969, pp. 169-178. | MR | Zbl

[Ma] U. Massari, Esistenza e Regolarità delle Ipersuperfici di Curvatura Media Assegnata in Rn, Arch. Rat. Mech. Anal., Vol. 55, 1974, pp. 357-382. | MR | Zbl

[Mo] C.B. Morrey, Second order elliptic systems of differential equations, Ann. of Math. Studies, No. 33, Princeton Univ. Press, 1954, pp. 101-159. | MR | Zbl

[Si] L. Simon, Lectures on geometric measure theory, Proceedings C.M.A. 3, Canberra, 1983. | MR | Zbl

[St1] K. Steffen, Isoperimetric inequalities and the problem of Plateau, Math. Ann., Vol. 222, 1976, pp. 97-144. | MR | Zbl

[St2] K. Steffen, On the existence of surfaces with prescribed mean curvature and boundary, Math. Z., Vol. 146, 1976, pp. 113-135. | MR | Zbl