no. 2
Smoothness and analyticity of free boundaries in variational inequalities
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 3 (1976) no. 2, pp. 289-310. 
@article{ASNSP_1976_4_3_2_289_0,
     author = {Caffarelli, Luis and Rivi\`ere, N. M.},
     title = {Smoothness and analyticity of free boundaries in variational inequalities},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {289--310},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 3},
     number = {2},
     year = {1976},
     zbl = {0363.35009},
     mrnumber = {412940},
     language = {en},
     url = {archive.numdam.org/item/ASNSP_1976_4_3_2_289_0/}
}
Caffarelli, L. A.; Rivière, N. M. Smoothness and analyticity of free boundaries in variational inequalities. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 3 (1976) no. 2, pp. 289-310. http://archive.numdam.org/item/ASNSP_1976_4_3_2_289_0/

[1] H. Brézis - D. Kinderlehrer, The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. Jour., 23, 9 (March 1974), pp. 831-844. | MR 361436 | Zbl 0278.49011

[2] L.A. Caffarelli - N.M. Rivière, On the rectifiability of domains with finite perimeter, Ann. Scuola Norm. Sup. Pisa, same issue, pp. 177-186. | Numdam | MR 410539 | Zbl 0362.49031

[3] J. Frehse, On the regularity of the solutions of a second order variational inequality, Boll. U.M.I., IV, 6 (1972), pp. 312-315. | MR 318650 | Zbl 0261.49021

[4] A. Friedman - K. Kinderlehrer, A one phase Stefan problem, to appear. | Zbl 0334.49002

[5] D. Kinderlehrer, The coincidence set of solutions of certain variational inequalities, Arch. Rat. Mech. and Anal., 40, 3 (1971), pp. 321-250. | MR 271799 | Zbl 0219.49014

[6] D. Kinderlehrer, How a minimal surface leaves an obstacle, Acta. Math., 430 (1973), pp. 221-242. | MR 419997 | Zbl 0268.49050

[7] D. Kinderlehrer, The free boundary determined by the solution to a differential equation, Indiana Journ. of Math., to appear. | MR 393807 | Zbl 0336.35031

[8] H. Lewy, On minimal surfaces with partly free boundary, Comm. Pure and Appl. Math., 4 (1951), pp. 1-13. | MR 52711

[9] H. Lewy, On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc., 65 (1959), pp. 37-58. | MR 104048 | Zbl 0089.08001

[10] H. Lewy, On the nature of the boundary separating two domains with different regimes, to appear.

[11] H. Lewy - G. Stampacchia, On the regularity of the solution of a variational inequality, Comm. Pure and Appl. Math., 22 (1969), pp. 153-188. | MR 247551 | Zbl 0167.11501

[12] A. Mcnabb, Strong comparison theorems for elliptic equations of second order, J. Math. Mech., 10 (1961), pp. 431-440. | MR 142881 | Zbl 0106.29903