@article{BUMI_2012_9_5_2_263_0,
author = {Sandro Salsa},
title = {Viscosity Solutions of Two-Phase Free Boundary Problems for Elliptic and Parabolic Operators},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {5},
year = {2012},
pages = {263-280},
zbl = {1264.35096},
mrnumber = {2977249},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_2_263_0}
}
Salsa, Sandro. Viscosity Solutions of Two-Phase Free Boundary Problems for Elliptic and Parabolic Operators. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 263-280. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_2_263_0/
[1] - , Existence and regularity for a minimum problem with free boundary, J. Reine und Angew. Math., 331, no. 1 (1982), 105-144. | MR 618549 | Zbl 0449.35105
[2] - - , Variational problems with two phases and their free boundaries, T. A.M.S., 282, no. 2 (1984)), 431-461. | MR 732100 | Zbl 0844.35137
[3] - , Flat free boundaries regularity in two-phase problems for a class of fully nonlinear elliptic operators with variable coefficients, Interfaces Free Bound., 11 (2009), 177-199. | MR 2511639 | Zbl 1179.35349
[4] - , Green's function, caloric measure and Fatou theorems for non-divergence parabolic equations in non-cylindrical domains, Forum Math., 20 (2008), 213-237. | MR 2394920 | Zbl 1165.35005
[5] - , The Dirichlet problem for second order parabolic operators in non-cylindrical domains, Math. Nachrichten., vol 283, n. 4 (2010), 522-542. | MR 2649367 | Zbl 1197.35130
[6] - - , Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems, Ann. Math., 143 (1996), 413-434. | MR 1394964 | Zbl 0853.35049
[7] - - , Regularity of the free boundary in parabolic phase-transition problems, Acta Math., 176, no. 2 (1996), 245-282. | MR 1397563 | Zbl 0891.35164
[8] - - , Phase-transition problems of parabolic type: flat free boundaries are smooth, Comm. Pure Appl. Math., 51 (1998), 77-112. | MR 1486632 | Zbl 0924.35197
[9] , A Harnack inequality approach to the regularity of free boundaries, Part 1: Lipschitz free boundaries are , Revista Matematica Iberoamericana, 3 (1987), 139-162. | MR 990856 | Zbl 0676.35085
[10] , A Harnack inequality approach to the regularity of free boundaries. II. Flat free boundaries are Lipschitz, Comm. Pure Appl. Math., 42, no. 1 (1989), 55- 78. | MR 973745 | Zbl 0676.35086
[11] , A Harnack inequality approach to the regularity of free boundaries, Part III: Existence theory, compactness and dependence on X. Ann. Sc. Norm. Sup. Pisa Cl. SC. (4), 15 (1988), 383-602. | MR 1029856
[12] - - , Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are . Arch. Rational Mech. Anal., 171 (2004), 329-348. | MR 2038343 | Zbl 1106.35144
[13] - , A geometric approach to free boundary problems. Graduate Studies in Mathematics, 68. American Mathematical Society, Providence, RI, 2005. x+270 pp. | MR 2145284 | Zbl 1083.35001
[14] , Free boundary regularity for a problem with right hand side, to appear on Interphases and Free Boundaries. | MR 2813524 | Zbl 1219.35372
[15] - - - , Fatou Theorems for some nonlinear elliptic equations, Rev. Mat. Iberoamericana, 4 (1988) 227-251. | MR 1028741 | Zbl 0703.35058
[16] , Two-phase problems for a class of fully nonlinear elliptic operators. Lipschitz free boundaries are , American Journal of Mathematics, 128, no. 3 (2006), 541-571. | MR 2230916 | Zbl 1142.35108
[17] , Regularity for nonisotropic two-phase problems with Lipschitz free boundaries. Differential Integral Equations, 10, no. 6 (1997), 1171-1179. | MR 1608061 | Zbl 0940.35047
[18] , Regularity of Lipschitz free boundaries in two-phase problems for fully nonlinear elliptic equations, Indiana Univ. Math. J., 50, no. 3 (2001), 1171-1200. | MR 1871352 | Zbl 1037.35104
[19] - , Regularity of the free boundary in two-phase problems for linear elliptic operators, Advances in Math., 214 (2007), 288-322. | MR 2348032 | Zbl 1189.35385
[20] - , Subsolutions of elliptic operators in divergence form and application to two-phase free boundary problem, Boundary Value Problems, vol. 2007 (2007) ID 21425. | MR 2291927 | Zbl 1188.35070
[21] - , Regularity of the solutions for parabolic two phase free boundary problems, Comm. Part. Diff. Equations, 354 (2010), 1095-1129. | MR 2753629 | Zbl 1193.35256
[22] - , Two-phase problems for parabolic operators: smoothness of the front, preprint 288-322. | MR 3139425 | Zbl 1189.35385
[23] , Variational Principles and Free Boundary problems, Wiley, New York, 1970. | MR 679313
[24] - , On the uniqueness of a solution of a two phase free boundary problem, Journal of Functional Analysis, 258 (2010), 2817-2833. | MR 2593345 | Zbl 1185.35340
[25] - , Viscosity solutions for the two phase Stefan Problem, Comm. Part. Diff. Eq., 36 (2011), 42-66. | MR 2763347 | Zbl 1216.35181
[26] - - , Existence of analytic solutions for the classical Stefan problem, Math. Ann., 338 (2007), 703-755. | MR 2317935 | Zbl 1130.35136
[27] , Regularity in free boundary problems, Conferenze del Seminario di Matematica, Università di Bari, 270 (1997). | MR 1638198 | Zbl 1045.35112
[28] , Numerical Methods for Phase Transition Problems, B.U.M.I. (8), 1-B (1998) 83-108. | MR 1619039 | Zbl 0896.65064
[29] , Regularity of free boundaries of two-phase problems for fully nonlinear elliptic equations of second order. I. Lipschitz free boundaries are , Comm. Pure Appl. Math., 53, no. 7 (2000), 799-810. | MR 1752439 | Zbl 1040.35158
[30] , Regularity of free boundaries of two-phase problems for fully nonlinear elliptic equations of second order. II. Flat free boundaries are Lipschitz, Comm. in Partial Differential equations, 27(7-8), no. 7 (2002), 1497-1514. | MR 1924475 | Zbl 1125.35424
[31] , Existence of solutions of two-phase free boundary for fully non linear equations of second order, J. of Geometric Analysis, no. 7 (2002), 1497-1514. | MR 2005161 | Zbl 1125.35424