Free boundary regularity for a problem with right hand side

Interfaces and Free Boundaries

Volumn 13, Issue 2, 2011, Pages 223-238

  De Silva, D ^a  

^a Program on US Russia Relations at Columbia s Harriman Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79959402943     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/255     Document Type: Article

References (20)

1. [AC] ALT, H. W., & CAFFARELLI, L. A. Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math. 325 (1981), 105-144. Zbl 0449.35105 MR 0618549
2. [AFT] AMICK, C. J., FRAENKEL, L. E., & TOLAND, J. F. On the Stokes conjecture for the wave of extreme form. Acta Math. 148 (1982), 193-214. Zbl 0495.76021 MR 0666110
3. [AF] ARGIOLAS, R., & FERRARI, F. Flat free boundaries regularity in two-phase problems for a class of fully nonlinear elliptic operators with variable coefficients. Interfaces Free Bound. 11 (2009), 177-199. Zbl 1179.35349 MR 2511639
4. 1,α. Rev. Mat. Iberoamer. 3 (1987), 139-162. Zbl 0676.35085 MR 0990856
5. [C2] CAFFARELLI, L. A. 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 0676.35086 MR 0973745
6. [CC] CAFFARELLI, L. A., & CABRÉ, X. Fully Nonlinear Elliptic Equations. Amer. Math. Soc. Colloq. Publ. 43, Amer. Math. Soc., Providence, RI (1995). Zbl 0834.35002 MR 1351007
7. 1,γ. Arch. Ration. Mech. Anal. 171 (2004), 329-348. Zbl 1106.35144 MR 2038343 (Pubitemid 38389766)
8. [CS] CONSTANTIN, A., & STRAUSS, W. Exact steady periodic water waves with vorticity. Comm. Pure Appl. Math. 57 (2004), 481-527. Zbl 1038.76011 MR 2027299
9. [F1] FELDMAN, M. Regularity of Lipschitz free boundaries in two-phase problems for fully nonlinear elliptic equations. Indiana Univ. Math. J. 50 (2001), 1171-1200. Zbl 1037.35104 MR 1871352 (Pubitemid 33583280)
10. [F2] FELDMAN, M. Regularity for nonisotropic two-phase problems with Lipshitz free boundaries. Differential Integral Equations 10 (1997), 1171-1179. Zbl 0940.35047 MR 1608061
11. 1,γ;. Amer. J. Math. 128 (2006), 541-571. Zbl 1142.35108 MR 2230916 (Pubitemid 43972481)
12. [FS1] FERRARI, F., & SALSA, S. Regularity of the free boundary in two-phase problems for elliptic operators. Adv. Math. 214 (2007), 288-322. Zbl 1189.35385 MR 2348032
13. [FS2] FERRARI, F., & SALSA, S. Subsolutions of elliptic operators in divergence form and application to two-phase free boundary problems. Bound. Value Probl. 2007, art. ID 57049, 21 pp. Zbl 1188.35070 MR 2291927
14. [KN] KINDERLEHRER, D., & NIRENBERG, L. Analyticity at the boundary of solutions of nonlinear second-order parabolic equations. Comm. Pure Appl. Math. 31 (1978), 283-338. Zbl 0391.35045 MR 0460897
15. [P] PLOTNIKOV, P. I. Proof of the Stokes conjecture in the theory of surface waves. Dinamika Splosh. Sredy 57 (1982), 41-76 (in Russian); English transl.: Stud. Appl. Math. 3 (2002), 217-244. Zbl 1152.76339 MR 1883094
16. [S] SAVIN, O. Small perturbation solutions for elliptic equations. Comm. Partial Differential Equations 32 (2007), 557-578. Zbl pre05174527 MR 2334822
17. [V] VARVARUCA, E. On the existence of extreme waves and the Stokes conjecture with vorticity. J. Differential Equations 246 (2009), 4043-4076. Zbl 1162.76011 MR 2514735
18. [VW] VARVARUCA, E., & WEISS, G. S. A geometric approach to generalized Stokes conjectures. Preprint 2009, arXiv:0908.1031.
19. 1,α. Comm. Pure Appl. Math. 53 (2000), 799-810. Zbl 1040.35158 MR 1752439
20. [W2] 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 (2002), 1497-1514. Zbl 1125.35424 MR 1924475