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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     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://archive.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://archive.numdam.org/item/ASNSP_1988_4_15_4_583_0/

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

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