Convexity and All-Time C∞-Regularity of the Interface in Flame Propagation

Communications on Pure and Applied Mathematics

Volumn 55, Issue 5, 2002, Pages 633-653

  Daskalopoulos, P ^a   Lee, K I Ahm ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036113466     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.10028     Document Type: Article

References (11)

1. Andreucci, D.; Gianni, R. Classical solutions to a multidimensional free boundary problem arising in combustion theory. Comm. Partial Differential Equations 19 (1994), no. 5-6, 803-826.
2. Caffarelli, L. A.; Vázquez, J. L. A free-boundary problem for the heat equation arising in flame propagation. Trans. Amer. Math. Soc. 347 (1995), no. 2, 411-441.
3. Caffarelli, L. A.; Spruck, J. Convexity properties of solutions to some classical variational problems. Comm. Partial Differential Equations 7 (1982), no. 11, 1337-1379.
4. Daskalopoulos, P.; Hamilton, R. Regularity of the free boundary for the porous medium equation. J. Amer. Math. Soc. 11 (1998), no. 4, 899-965.
5. Daskalopoulos, P.; Hamilton, R. The free boundary in the Gauss curvature flow with flat sides. J. Reine Angenw. Math. 510 (1999), 187-227.
6. ∞-regularity of the interface in degenerate diffusion: a geometric approach. Duke. Math. J. 108 (2001), no. 2, 295-327.
7. Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order. Second edition. Grundlehren der Mathematischen Wissenschaften, 224. Springer, Berlin, 1983.
8. Lieberman, G. M. Second order parabolic differential equations. World Scientific, River Edge, N.J., 1996.
9. Ladyzhenskaya, O. A.;Ural'tseva, N. N. Linear and quasilinear elliptic equations. Academic, New York-London, 1968.
10. Petrosyan, A. S. Convexity and uniqueness in a free boundary problem arising in combustion theory. Preprint.
11. Vázquez, J. L. The free boundary problem for the heat equation with fixed gradient condition. Free boundary problems, theory and applications (Zakopane, 1995), 277-302. Pitman Research Notes in Mathematics Series, 363. Longman, Harlow, 1996.