Citation: Gianmaria Verzini. Foreword to the special issue 'Contemporary PDEs between theory and modeling'[J]. Mathematics in Engineering, 2021, 3(1): i-iv. doi: 10.3934/mine.2021.i
[1] | Athanasopoulos I, Caffarelli L, Salsa S (1996) Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Ann Math, 143: 413-434. doi: 10.2307/2118531 |
[2] | Athanasopoulos I, Caffarelli L, Salsa S (1996) Regularity of the free boundary in parabolic phase-transition problems. Acta Math 176: 245-282. doi: 10.1007/BF02551583 |
[3] | Athanasopoulos I, Caffarelli LA, Kenig C, et al. (2001) An area-Dirichlet integral minimization problem. Commun Pure Appl Math 54: 479-499. doi: 10.1002/1097-0312(200104)54:4<479::AID-CPA3>3.0.CO;2-2 |
[4] | Athanasopoulos I, Caffarelli LA, Salsa S (1998) Phase transition problems of parabolic type: flat free boundaries are smooth. Commun Pure Appl Math 51: 77-112. doi: 10.1002/(SICI)1097-0312(199801)51:1<77::AID-CPA4>3.0.CO;2-C |
[5] | Athanasopoulos I, Caffarelli LA, Salsa S (2001) The free boundary in an inverse conductivity problem. J Reine Angew Math 534: 1-31. |
[6] | Athanasopoulos I, Caffarelli LA, Salsa S (2003) Stefan-like problems with curvature. J Geom Anal 13: 21-27. doi: 10.1007/BF02930993 |
[7] | Athanasopoulos I, Caffarelli LA, Salsa S (2008) The structure of the free boundary for lower dimensional obstacle problems. Am J Math 130: 485-498. doi: 10.1353/ajm.2008.0016 |
[8] | Athanasopoulos I, Salsa S (1991) An application of a parabolic comparison principle to free boundary problems. Indiana Univ Math J 40: 29-32. doi: 10.1512/iumj.1991.40.40002 |
[9] | Caffarelli L, Fabes E, Mortola S, et al. (1981) Boundary behavior of nonnegative solutions of elliptic operators in divergence form. Indiana Univ Math J 30: 621-640. doi: 10.1512/iumj.1981.30.30049 |
[10] | Caffarelli L, Salsa S (2005) A Geometric Approach to Free Boundary Problems, Providence, RI: American Mathematical Society. |
[11] | Caffarelli L, Silvestre L (2007), An extension problem related to the fractional Laplacian. Commun Part Diff Eq 32: 1245-1260. doi: 10.1080/03605300600987306 |
[12] | Caffarelli LA, Salsa S, Silvestre L (2008) Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Invent Math 171: 425-461. doi: 10.1007/s00222-007-0086-6 |
[13] | Cerutti MC, Ferrari F, Salsa S (2004) Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are $C^{1, \gamma}$. Arch Ration Mech Anal 171: 329-348. doi: 10.1007/s00205-003-0290-5 |
[14] | De Silva D, Ferrari F, Salsa S (2014) Two-phase problems with distributed sources: regularity of the free boundary. Anal PDE 7: 267-310. doi: 10.2140/apde.2014.7.267 |
[15] | De Silva D, Ferrari F, Salsa S (2015) Free boundary regularity for fully nonlinear non-homogeneous two-phase problems. J Math Pure Appl 103: 658-694. doi: 10.1016/j.matpur.2014.07.006 |
[16] | De Silva D, Ferrari F, Salsa S (2019) Regularity of higher order in two-phase free boundary problems. T Am Math Soc 371: 3691-3720. doi: 10.1090/tran/7550 |
[17] | Fabes E, Garofalo N, Marín-Malave S, et al. (1988) Fatou theorems for some nonlinear elliptic equations. Rev Mat Iberoamericana 4: 227-251. doi: 10.4171/RMI/73 |
[18] | Fabes E, Salsa S (1983) Estimates of caloric measure and the initial-{D}irichlet problem for the heat equation in Lipschitz cylinders. T Am Math Soc 279: 635-650. doi: 10.1090/S0002-9947-1983-0709573-7 |
[19] | Fabes EB, Garofalo N, Salsa S (1986) A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations. Illinois J Math 30: 536-565. doi: 10.1215/ijm/1256064230 |
[20] | Ferrari F, Salsa S (2007) Regularity of the free boundary in two-phase problems for linear elliptic operators. Adv Math 214: 288-322. doi: 10.1016/j.aim.2007.02.004 |
[21] | Ferrari F, Salsa S (2010) Regularity of the solutions for parabolic two-phase free boundary problems. Commun Part Diff Eq 35: 1095-1129. doi: 10.1080/03605301003717126 |
[22] | Ferrari F, Salsa S (2014) Two-phase free boundary problems for parabolic operators: smoothness of the front. Commun Pure Appl Math 67: 1-39. doi: 10.1002/cpa.21490 |
[23] | Laurence P, Salsa S (2009) Regularity of the free boundary of an American option on several assets. Commun Pure Appl Math 62: 969-994. doi: 10.1002/cpa.20268 |
[24] | Maderna C, Pagani CD, Salsa S (1986) Existence results in an inverse problem of potential theory. Nonlinear Anal 10: 277-298. doi: 10.1016/0362-546X(86)90004-0 |
[25] | Maderna C, Salsa S (1979) Symmetrization in Neumann problems. Appl Anal 9: 247-256. doi: 10.1080/00036817908839273 |
[26] | Pagani CD, Salsa S (1990) Analisi Matematica 1, Zanichelli. |
[27] | Pagani CD, Salsa S (1990) Analisi Matematica 2, Zanichelli. |
[28] | Salsa S (2016) Partial Differential Equations in Action: From Modelling to Theory, 3 Eds., Springer, 2016. |