@article{ASNSP_1998_4_27_2_253_0,
author = {Lederman, Claudia and Wolanski, Noemi},
title = {Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {253--288},
year = {1998},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 27},
number = {2},
mrnumber = {1664689},
zbl = {0931.35200},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1998_4_27_2_253_0/}
}
TY - JOUR AU - Lederman, Claudia AU - Wolanski, Noemi TI - Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1998 SP - 253 EP - 288 VL - 27 IS - 2 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1998_4_27_2_253_0/ LA - en ID - ASNSP_1998_4_27_2_253_0 ER -
%0 Journal Article %A Lederman, Claudia %A Wolanski, Noemi %T Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1998 %P 253-288 %V 27 %N 2 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1998_4_27_2_253_0/ %G en %F ASNSP_1998_4_27_2_253_0
Lederman, Claudia; Wolanski, Noemi. Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 27 (1998) no. 2, pp. 253-288. https://www.numdam.org/item/ASNSP_1998_4_27_2_253_0/
[1] - , Existence and regularity for a minimum problem with a free boundary, J. Reine Angew. Math. 325 (1981), 105-144. | Zbl | MR
[2] - - , Variational problems with two phases and their free boundaries, Trans. Amer. Math. Soc. 282 (1984), 431-461. | Zbl | MR
[3] - - , Uniform estimates for regularization offree boundary problems, In: "Analysis and Partial Differential Equations" (Cora Sadosky, ed.) Lecture Notes in Pure and Applied Mathematics vol. 122, Marcel Dekker, New York, 1988, pp. 567-619. | Zbl | MR
[4] - - , A convexity property of eigenvalues with applications, to appear. | MR
[5] - , "Theory of Laminar Flames", Cambridge University Press, Cambridge, 1982. | Zbl | MR
[6] , A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α, Rev. Mat. Iberoamericana 3 (1987), 139-162. | Zbl
[7] , A Harnack inequality approach to the regularity of free boundaries. Part II: Flat free boundaries are Lipschitz, Comm. Pure Appl. Math. 42 (1989), 55-78. | Zbl | MR
[8] , A Harnack inequality approach to the regularity of free boundaries. Part III: Existence theory, compactness and dependence on X, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), 583-602. | Zbl | MR | Numdam
[9] , A monotonicity formula for heat functions in disjoint domains, In: "Boundary Value Problems for P.D.E.'s and Applications", dedicated to E. Magenes (J. L. Lions, C. Baiocchi, eds.), Masson, Paris, 1993, pp. 53-60. | Zbl | MR
[10] , Uniform Lipschitz regularity of a singular perturbation problem, Differential Integral Equations 8 (1995), 1585-1590. | Zbl | MR
[11] - - , Uniform estimates and limits for a two phase parabolic singular perturbation problem, Indiana Univ. Math. J. 46 (1997), 453-490. | Zbl | MR
[12] - - , Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem, Indiana Univ. Math. J. 46 (1997), 719-740. | Zbl | MR
[13] - , A free boundary problem for the heat equation arising in flame propagation, Trans. Amer. Math. Soc. 347 (1995), 411-441. | Zbl | MR
[14] , "Geometric Measure Theory", Springer-Verlag, New York, 1969. | Zbl | MR
[15] - , "Measure Theory and Fine Properties of Functions", Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992. | Zbl | MR
[16] - - , Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem, J. Math. Pures Appl. 76 (1997), 563-608. | Zbl | MR
[17] - , Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 373-391. | Zbl | MR | Numdam
[18] , The free boundary problem for the heat equation with fixed gradient condition, In: "Free Boundary Problems, Theory and Applications" (M. Niezgodka, P. Strzelecki, eds.), Pitman Research Series in Mathematics vol. 363, Longman, 1996, pp. 277-302. | Zbl | MR





