Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

Inventiones Mathematicae

Volumn 171, Issue 2, 2008, Pages 425-461

  Caffarelli, Luis A ^a   Salsa, Sandro ^b   Silvestre, Luis ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b POLITECNICO DI MILANO   (Italy)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37849049246     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-007-0086-6     Document Type: Article

References (16)

1. Athanasopoulos, I., Caffarelli, L.A.: Optimal regularity of lower dimensional obstacle problems. Zap. Nauchn. Semin. POMI 310 (Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. 35 [34]), 49-66, 226 (2004)
2. Athanasopoulos, I., Caffarelli, L.A., Salsa, S.: The structure of the free boundary for lower dimesional obstacle problems. To appear in Am. J. Math. (2007)
3. Bouchaud, J.P., Georges, A.: Anomalous diffusion in disordered media: Statistical mechanics, models and physical applications. Phys. Rep. 195(4-5), 127-293 (1990)
4. Caffarelli, L.A.: The obstacle problem revisited. J. Fourier Anal. Appl. 4(4-5), 383-402 (1998)
5. Caffarelli, L.A., Cabré, X.: Fully Nonlinear Elliptic Equations. Colloq. Publ., Am. Math. Soc., vol. 43. Am. Math. Soc., Providence, RI (1995)
6. Caffarelli, L., Salsa, S.: A Geometric Approach to Free Boundary Problems. Grad. Stud. Math., vol. 68. Am. Math. Soc., Providence, RI (2005)
7. Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equations 32(8), 1245-1260 (2007)
8. Caffarelli, L., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Preprint
9. Constantin, P.: Euler equations, Navier-Stokes equations and turbulence. In: Mathematical Foundation of Turbulent Viscous Flows. Lect. Notes Math., vol. 1871, pp. 1-43. Springer, Berlin (2006)
10. Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman Hall/CRC Financ. Math. Ser. Chapman & Hall/CRC, Boca Raton, FL (2004)
11. Fabes, E.B., Kenig, C.E., Jerison, D.: Boundary behavior of solutions to degenerate elliptic equations. In: Conference on Harmonic Analysis in Honor of Antoni Zygmund, vol. I, II (Chicago, Ill., 1981), Wadsworth Math. Ser., pp. 577-589. Wadsworth, Belmont, CA (1983)
12. Fabes, E.B., Kenig, C.E., Serapioni, R.P.: The local regularity of solutions of degenerate elliptic equations. Commun. Partial Differ. Equations 7(1), 77-116 (1982)
13. Garofalo, N.: Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension. J. Differ. Equations 104(1), 117-146 (1993)
14. Kilpeläinen, T.: Smooth approximation in weighted Sobolev spaces. Commentat. Math. Univ. Carol. 38(1), 29-35 (1997)
15. Milakis, E., Silvestre, L.E.: Regularity for fully nonlinear elliptic equations with Neumann boundary data. Commun. Partial Differ. Equations 31(7-9), 1227-1252 (2006)
16. Silvestre, L.: The regularity of the obstacle problem for a fractional power of the Laplace operator. Commun. Pure Appl. Math. 60(1), 67-112 (2007)