Geodesic
Viscosity Solutions of Two-Phase Free Boundary Problems for Elliptic and Parabolic Operators
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 263-280.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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Salsa, Sandro. Viscosity Solutions of Two-Phase Free Boundary Problems for Elliptic and Parabolic Operators. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 2, pp. 263-280. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_2_a5/

[1] H. W. Alt - L. Caffarelli, Existence and regularity for a minimum problem with free boundary, J. Reine und Angew. Math., 331, no. 1 (1982), 105-144. | fulltext EuDML | MR | Zbl

[2] H. W. Alt - L. Caffarelli - A. Friedman, Variational problems with two phases and their free boundaries, T. A.M.S., 282, no. 2 (1984)), 431-461. | DOI | MR | Zbl

[3] R. Argiolas - F. Ferrari, 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. | DOI | MR | Zbl

[4] R. Argiolas - A. Grimaldi, Green's function, caloric measure and Fatou theorems for non-divergence parabolic equations in non-cylindrical domains, Forum Math., 20 (2008), 213-237. | DOI | MR | Zbl

[5] R. Argiolas - A. Grimaldi, The Dirichlet problem for second order parabolic operators in non-cylindrical domains, Math. Nachrichten., vol 283, n. 4 (2010), 522-542. | DOI | MR | Zbl

[6] Athanasopoulos - L. Caffarelli - S. Salsa, Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems, Ann. Math., 143 (1996), 413-434. | DOI | MR | Zbl

[7] Athanasopoulos - L. Caffarelli - S. Salsa, Regularity of the free boundary in parabolic phase-transition problems, Acta Math., 176, no. 2 (1996), 245-282. | DOI | MR | Zbl

[8] Athanasopoulos - L. Caffarelli - S. Salsa, Phase-transition problems of parabolic type: flat free boundaries are smooth, Comm. Pure Appl. Math., 51 (1998), 77-112. | DOI | MR | Zbl

[9] L. Caffarelli, A Harnack inequality approach to the regularity of free boundaries, Part 1: Lipschitz free boundaries are $C_{\alpha}^1$, Revista Matematica Iberoamericana, 3 (1987), 139-162. | fulltext EuDML | DOI | MR | Zbl

[10] L. Caffarelli, 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. | DOI | MR | Zbl

[11] L. Caffarelli, 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. | fulltext EuDML | MR

[12] M. C. Cerutti - F. Ferrari - S. Salsa, Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are $C^{1;\gamma}$. Arch. Rational Mech. Anal., 171 (2004), 329-348. | DOI | MR | Zbl

[13] L. Caffarelli - S. Salsa, A geometric approach to free boundary problems. Graduate Studies in Mathematics, 68. American Mathematical Society, Providence, RI, 2005. x+270 pp. | DOI | MR | Zbl

[14] D. De Silva, Free boundary regularity for a problem with right hand side, to appear on Interphases and Free Boundaries. | DOI | MR | Zbl

[15] E. Fabes - N. Garofalo - M. Malave - S. Salsa, Fatou Theorems for some nonlinear elliptic equations, Rev. Mat. Iberoamericana, 4 (1988) 227-251. | fulltext EuDML | DOI | MR | Zbl

[16] F. Ferrari, Two-phase problems for a class of fully nonlinear elliptic operators. Lipschitz free boundaries are $C^{1;\gamma}$, American Journal of Mathematics, 128, no. 3 (2006), 541-571. | MR | Zbl

[17] M. Feldman, Regularity for nonisotropic two-phase problems with Lipschitz free boundaries. Differential Integral Equations, 10, no. 6 (1997), 1171-1179. | MR | Zbl

[18] M. Feldman, Regularity of Lipschitz free boundaries in two-phase problems for fully nonlinear elliptic equations, Indiana Univ. Math. J., 50, no. 3 (2001), 1171-1200. | DOI | MR | Zbl

[19] F. Ferrari - S. Salsa, Regularity of the free boundary in two-phase problems for linear elliptic operators, Advances in Math., 214 (2007), 288-322. | DOI | MR | Zbl

[20] F. Ferrari - S. Salsa, Subsolutions of elliptic operators in divergence form and application to two-phase free boundary problem, Boundary Value Problems, vol. 2007 (2007) ID 21425. | fulltext EuDML | DOI | MR | Zbl

[21] F. Ferrari - S. Salsa, Regularity of the solutions for parabolic two phase free boundary problems, Comm. Part. Diff. Equations, 354 (2010), 1095-1129. | DOI | MR | Zbl

[22] F. Ferrari - S. Salsa, Two-phase problems for parabolic operators: smoothness of the front, preprint 288-322. | DOI | MR | Zbl

[23] A. Friedman, Variational Principles and Free Boundary problems, Wiley, New York, 1970. | MR

[24] G. Lu - P. Wang, On the uniqueness of a solution of a two phase free boundary problem, Journal of Functional Analysis, 258 (2010), 2817-2833. | DOI | MR | Zbl

[25] I. C. Kim - N. Pozar, Viscosity solutions for the two phase Stefan Problem, Comm. Part. Diff. Eq., 36 (2011), 42-66. | DOI | MR | Zbl

[26] J. Prüss - J. Saal - G. Simonett, Existence of analytic solutions for the classical Stefan problem, Math. Ann., 338 (2007), 703-755. | DOI | MR | Zbl

[27] S. Salsa, Regularity in free boundary problems, Conferenze del Seminario di Matematica, Università di Bari, 270 (1997). | MR | Zbl

[28] C. Verdi, Numerical Methods for Phase Transition Problems, B.U.M.I. (8), 1-B (1998) 83-108. | fulltext bdim | fulltext EuDML | MR | Zbl

[29] P. Y. Wang, Regularity of free boundaries of two-phase problems for fully nonlinear elliptic equations of second order. I. Lipschitz free boundaries are $C^{1;\alpha}$, Comm. Pure Appl. Math., 53, no. 7 (2000), 799-810. | DOI | MR | Zbl

[30] P. Y. Wang, 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. | DOI | MR | Zbl

[31] P. Y. Wang, 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. | DOI | MR | Zbl