Regularity of the free boundary in two-phase problems for linear elliptic operators

Advances in Mathematics

Volumn 214, Issue 1, 2007, Pages 288-322

  Ferrari, Fausto ^a,b   Salsa, Sandro ^c  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b CIRAM   (Italy)

^c POLITECNICO DI MILANO   (Italy)

Author keywords

Elliptic operators; Free boundary; Strict monotonicity; Two phase problems

Indexed keywords

EID: 34250191454     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2007.02.004     Document Type: Article

References (14)

1. Athanasopoulos I., Caffarelli L., and Salsa S. Phase transition problems of parabolic type: Flat free boundaries are smooth. Comm. Pure Appl. Math. 51 1 (1998) 77-112
2. Caffarelli L. 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
3. Caffarelli L.A. A Harnack inequality approach to the regularity of free boundaries. III. Existence theory, compactness, and dependence on X. Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 15 4 (1988) 583-602
4. Caffarelli L., and Cabré X. Fully Nonlinear Elliptic Equations. Amer. Math. Soc. Colloq. Publ. vol. 43 (1995), Amer. Math. Soc., Providence, RI vi+104 pp
5. Caffarelli L., and Salsa S. A geometric approach to free boundary problems. Grad. Stud. Math. vol. 68 (2005), Amer. Math. Soc., Providence, RI x+270 pp
6. Caffarelli L., Crandall M.G., Kocan M., and Świȩch A. On viscosity solutions of fully nonlinear equations with measurable ingredients. Comm. Pure Appl. Math. 49 4 (1996) 365-397
7. 1, γ. Arch. Ration. Mech. Anal. 171 (2004) 329-348
8. Fabes E., Garofalo N., Marin-Malave S., and Salsa S. Fatou theorems for some nonlinear elliptic equations. Rev. Mat. Iberoamericana 4 2 (1988) 227-251
9. Feldman M. Regularity of Lipschitz free boundaries in two-phase problems for fully nonlinear elliptic equations. Indiana Univ. Math. J. 50 3 (2001) 1171-1200
10. 1, γ. Amer. J. Math. 128 (2006) 541-571
11. Miller K. Barriers on cones for uniformly elliptic operators. Ann. Mat. Pura Appl. (4) 76 (1967) 93-105
12. 1, p-interior estimates for solutions of fully nonlinear, uniformly elliptic equations. Adv. Differential Equations 2 6 (1997) 1005-1027
13. E. Teixeira, A variational treatment for elliptic equation of the flame propagation type: Regularity of the free boundary, preprint, 2005
14. Wang P.Y. Regularity of free boundaries of two-phase problems for fully nonlinear elliptic equations of second order. II. Flat free boundaries are Lipschitz. Comm. Partial Differential Equations 27(7-8) 7 (2002) 1497-1514