Star shaped coincidence sets in the obstacle problem
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 11 (1984) no. 1, p. 123-128 
@article{ASNSP_1984_4_11_1_123_0,
     author = {Sakaguchi, Shigeru},
     title = {Star shaped coincidence sets in the obstacle problem},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 11},
     number = {1},
     year = {1984},
     pages = {123-128},
     zbl = {0539.49004},
     mrnumber = {752582},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1984_4_11_1_123_0}
}

Sakaguchi, Shigeru. Star shaped coincidence sets in the obstacle problem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 11 (1984) no. 1, pp. 123-128. http://www.numdam.org/item/ASNSP_1984_4_11_1_123_0/

[1] H. Brezis - D. Kinderlehrer, The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. J., 23 (1974), pp. 831-841. | MR 361436 | Zbl 0278.49011

[2] L.A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math., 139 (1978), pp. 155-184. | MR 454350 | Zbl 0386.35046

[3] L.A. Caffarelli - D. Kinderlehrer, Potential methods in variational inequalities, J. D'Analyse Math., 37 (1980), pp. 285-295. | MR 583641 | Zbl 0455.49010

[4] L.A. Caffarelli - J. Spruck, Convexity properties of solutions to some classical variational problems, Comm. P.D.E., 7 (1982), pp. 1337-1379. | MR 678504 | Zbl 0508.49013

[5] A. Friedmar - D. Kinderlehrer, A one phase Stefan problem, Indiana Univ. Math. J., 24 (1975), pp. 1005-1035. | Zbl 0334.49002

[6] D. Kinderlehrer, The coincidence set of solutions of certain variational inequalities, Arch. Rational Mech. Anal., 40 (1971), pp. 231-250. | MR 271799 | Zbl 0219.49014

[7] D. Kinderlehrer - L. Nirenberg, Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa, Ser. IV, 4 (1977), pp. 373-391. | Numdam | MR 440187 | Zbl 0352.35023

[8] D. Kinderlehrer - G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York-London-Toronto- Sydney-San Francisco, 1980. | MR 567696 | Zbl 0457.35001

[9] H. Lewy, An inversion of the obstacle problem and its explicit solution, Ann. Scuola Norm. Sup. Pisa, Ser. IV, 6 (1979), pp. 561-571. | Numdam | MR 563334 | Zbl 0428.35080

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