Allard type regularity results for varifolds with free boundaries
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 13 (1986) no. 1, p. 129-169 
@article{ASNSP_1986_4_13_1_129_0,
     author = {Gr\"uter, Michael and Jost, J\"urgen},
     title = {Allard type regularity results for varifolds with free boundaries},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 13},
     number = {1},
     year = {1986},
     pages = {129-169},
     zbl = {0615.49018},
     mrnumber = {863638},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1986_4_13_1_129_0}
}

Grüter, Michael; Jost, Jürgen. Allard type regularity results for varifolds with free boundaries. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 13 (1986) no. 1, pp. 129-169. http://www.numdam.org/item/ASNSP_1986_4_13_1_129_0/

[AW1] W.K. Allard, On the first variation of a varifold, Ann. Math., 95 (1972), 417-491. | MR 307015 | Zbl 0252.49028

[AW2] W.K. Allard, On the first variation of a varifold: boundary behavior, Ann. Math., 101 (1975), 418-446. | MR 397520 | Zbl 0319.49026

[DJ] J. Duggan, Regularity theorems for varifolds with mean curvature, Ph.D. thesis, Australian National University, 1984. | MR 799216

[FH] H. Federer, Geometric measure theory, Springer-Verlag, Berlin-Heidelberg -New York, 1969. | MR 257325 | Zbl 0176.00801

[GJ] M. Grüter - J. Jost, On embedded minimal disks in convex bodies, to appear in: Analyse non Linéaire. | Numdam | MR 868522 | Zbl 0617.49017

[SL] L. Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, Vol. 3, 1983. | MR 756417 | Zbl 0546.49019