Uniform Hölder estimates in a class of elliptic systems and applications to singular limits in models for diffusion flames

Archive for Rational Mechanics and Analysis

Volumn 183, Issue 3, 2007, Pages 457-487

  Caffarelli, Luis A ^a   Roquejoffre, Jean Michel ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846815194     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-006-0013-9     Document Type: Article

References (20)

1. BARLES, G. PERTHAME, B.: Exit time problems in optimal control and vanishing viscosity method. SIAM J. Control Optim. 26, 1133-1148 (1988)
2. BERESTYCKI, H., CAFFARELLI, L.A., NIRENBERG, L.: Uniform estimates for regularizations of free boundary problems. Analysis and Partial Differential Equations (SADOVSKY ed.). Lecture Notes in Pure and Applied Mathematics, 122, 567-619, 1990
3. BERESTYCKI, H., NIRENBERG, L.: On the method of moving planes and the sliding method. Bull Braz. Math. Soc. (N.S) 22, 1-37 (1991)
4. BERESTYCKI, H., NIRENBERG, L., VARADHAN, S.R.S.: The principal eigenvalue and Maximum principle for second order elliptic operators in general domains. Comm. Pure Appl. Math. 47, 47-92 (1994)
5. BURKE, S.P. SCHUMANN T.E.W.: Diffusion flames. Industr. Engng Chem. 20, 998-1004 (1928)
6. CAFFARELLI, L.A.: Uniform Lipschitz regularity of a singular perturbation problem. Differential Integral Equations 8, 1585-1590 (1995)
7. CAFFARELLI, L. A.: A Harnack inequality approach to the regularity of free boundaries. III. Existence theory, compactness, and dependence on X.Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15, 583-602 (1989)
8. CAFFARELLI, L.A., JERISON, D., KENIG, C.E.: Some new monotonicity theorems with applications to free boundary problems. Ann. of Math. 155, 369-404 (2002)
9. CAFFARELLI, L.A., SALSA, S.: A Geometric Approach to free Boundary Problems. Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2005
10. CONTI, M., TERRACINI, S., VERZINI, G.: Asymptotic estimates for the spatial segregation of competitive systems. Adv. Math. 195, 524-560 (2005)
11. DOLD, J.W.: Flame propagation in a nonuniform mixture: analysis of a slowly varying triple flame. Comb. Flame 76, 71-88 (1989)
12. FENDELL, F.E.: Ignition and extinction in combustion of initially unmixed reactants. J. Fluid Mech. 21, 281-303 (1965)
13. GRISVARD, P.: Singularities in Boundary Value Problems. Springer-Verlag, Berlin, 1992
14. JONES, C.K.R.T.: Geometric singular perturbation theory. Dynamical systems (Montecatini Terme, 1994), pp. 44-118, Lecture Notes in Mathematics, Springer, Berlin, 1995
15. KINDERLEHRER, D., SPRUCK, J.: The shape and smoothness of stable plasma configurations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 5, 131-148 (1978)
16. KINDERLEHRER, D., STAMPACCHIA, G.: An Introduction to Variational Inequalities and their Applications. Pure and Applied Mathematics. Academic Press, Inc. New York, 1980
17. LITTMAN, W., STAMPACCHIA, G., WEINBERGER, H.F.: Regular points for elliptic equations with discontinuous coefficients. Ann. Sc. Norm. Super. Pisa. Sci. (5) 17, 43-77 (1963)
18. LIÑAN, A.: The asymptotic structure of counterflow diffusion flames. Acta Astronaut. 1, 1007-1039 (1974)
19. SMOLLER, J.: Shock Waves and Reaction Diffusion Equations. Springer, 1990
20. WILLIAMS, F.A.: Combustion Theory. Benjamin-Cummings, Menlo Park, New York, 1985