A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
Teixeira, Eduardo V.
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 633-658 / Harvested from Numdam
@article{AIHPC_2008__25_4_633_0,
     author = {Teixeira, Eduardo V.},
     title = {A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {633-658},
     doi = {10.1016/j.anihpc.2007.02.006},
     mrnumber = {2436786},
     zbl = {pre05306973},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_4_633_0}
}
Teixeira, Eduardo V. A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 633-658. doi : 10.1016/j.anihpc.2007.02.006. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_4_633_0/

[1] Alt H., Caffarelli L., Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math. 325 (1981) 105-144. | MR 618549 | Zbl 0449.35105

[2] Berestycki H., Caffarelli L.A., Nirenberg L., Uniform estimates for regularization of free boundary problems, in: Analysis and Partial Differential Equations, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990, pp. 567-619. | MR 1044809 | Zbl 0702.35252

[3] Berestycki H., Nirenberg L., Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations, J. Geom. Phys. 5 (2) (1988) 237-275. | MR 1029429 | Zbl 0698.35031

[4] Berestycki H., Nirenberg L., Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains, in: Analysis, et cetera, Academic Press, Boston, MA, 1990, pp. 115-164. | MR 1039342 | Zbl 0705.35004

[5] Berestycki H., Nirenberg L., Travelling front solutions of semilinear equations in n dimensions, in: Frontiers in Pure and Applied Mathematics, North-Holland, Amsterdam, 1991, pp. 31-41. | MR 1110590 | Zbl 0780.35054

[6] Berestycki H., Nirenberg L., On the method of moving planes and the sliding method, Bol. Soc. Brasil. Mat. (N.S.) 22 (1) (1991) 1-37. | MR 1159383 | Zbl 0784.35025

[7] Caffarelli L.A., A Harnack inequality approach to the regularity of free boundaries. I. Lipschitz free boundaries are C 1,α , Rev. Mat. Iberoamericana 3 (2) (1987) 139-162. | MR 990856 | Zbl 0676.35085

[8] Caffarelli L.A., A Harnack inequality approach to the regularity of free boundaries. II. Flat free boundaries are Lipschitz, Comm. Pure Appl. Math. 42 (1) (1989) 55-78. | MR 973745 | Zbl 0676.35086

[9] Caffarelli L.A., A Harnack inequality approach to the regularity of free boundaries. III. Existence theory, compactness, and dependence on X, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (4) (1988) 583-602, (1989). | Numdam | MR 1029856 | Zbl 0702.35249

[10] Caffarelli L.A., Jerison D., Kenig C.E., Some new monotonicity theorems with applications to free boundary problems, Ann. of Math. (2) 155 (2) (2002) 369-404. | MR 1906591 | Zbl 1142.35382

[11] Caffarelli L.A., Lederman C., Wolanski N., Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem, Indiana Univ. Math. J. 46 (3) (1997) 719-740. | MR 1488334 | Zbl 0909.35013

[12] Cerutti M.C., Ferrari F., Salsa S., Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are C 1,γ , Arch. Ration. Mech. Anal. 171 (2004) 329-348. | MR 2038343 | Zbl 1106.35144

[13] Ferrari F., Salsa S., Regularity of the free boundary in two-phase problems for linear elliptic operators, Adv. Math. 214 (1) (2007) 288-322. | MR 2348032 | Zbl pre05180273

[14] Fife P.C., Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomath., vol. 28, Springer-Verlag, New York, 1979. | MR 527914 | Zbl 0403.92004

[15] Giaquinta M., Giusti E., Quasi-Minima, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 79-107. | Numdam | MR 778969 | Zbl 0541.49008

[16] Han Q., Lin F., Elliptic Partial Differential Equations, Courant Lecture Notes in Mathematics, vol. 1, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 1997. | MR 1669352 | Zbl 1052.35505

[17] Lederman C., Wolanski N., Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 27 (2) (1998) 253-288, (1999). | Numdam | MR 1664689 | Zbl 0931.35200

[18] Moreira D., Teixeira E.V., A singular free boundary problem for elliptic equations in divergence form, Calc. Var. Partial Differential Equations 29 (2) (2007) 161-190. | MR 2307771 | Zbl pre05146201

[19] E.V. Teixeira, Optimal regularity of viscosity solutions of fully nonlinear singular equations and their limiting free boundary problems, Mat. Contemp., submitted for publication. | MR 2373512 | Zbl 1159.49037

[20] Weiss G.S., Partial regularity for a minimum problem with free boundary, J. Geom. Anal. 9 (2) (1999) 317-326. | MR 1759450 | Zbl 0960.49026