no. 4
A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on X
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 4, pp. 583-602. 
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     author = {Caffarelli, Luis A.},
     title = {A {Harnack} inequality approach to the regularity of free boundaries. {Part} {III} : existence theory, compactness, and dependence on $X$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {583--602},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 15},
     number = {4},
     year = {1988},
     mrnumber = {1029856},
     zbl = {0702.35249},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1988_4_15_4_583_0/}
}
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Caffarelli, Luis A. A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on $X$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 15 (1988) no. 4, pp. 583-602. http://www.numdam.org/item/ASNSP_1988_4_15_4_583_0/

[A-C] H.W. Alt - L.A. Caffarelli, Existence and Regularity for a minimal problem with a free boundary, J. Reine Angew. Math 325 (1981), 105-144. | MR | Zbl

[A-C-F] H.W. Alt - L.A. Caffarelli - A. Friedman, Variational problems with two phases and their free boundaries, T.A.M.S. 282 No. 2 (1984), 431-461. | MR | Zbl

[C,I] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α, Revista Matematica Iberoamericana, to appear.

[C,II] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part II: Flat free boundaries are Lipschitz, to appear.

[L-S-W] W. Littman - G. Stampacchia - H. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. di Pisa (3) 17 (1963), 43-77. | Numdam | MR | Zbl

[G] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, 1984. | MR | Zbl

[G-T]J. Gilbarg - Trudinger, Elliptic P.D.E. of Second order, 2nd Ed., Springer, New York, 1983.