Cσ+α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels

Calculus of Variations and Partial Differential Equations

Volumn 54, Issue 4, 2015, Pages 3571-3601

  Serra, Joaquim ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

35J60; 45K05

Indexed keywords

EID: 84947864016     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-015-0914-2     Document Type: Article

References (15)

1. Caffarelli, L.A.: Interior a priori estimates for solutions of fully nonlinear equations. Ann. Math. 130, 189–213 (1989)
2. Caffarelli, L., Cabré, X.: Fully nonlinear elliptic equations. In: American Mathematical Society Colloquium Publications, vol. 43. American Mathematical Society, Providence (1995)
3. Caffarelli, L., Silvestre, L.: Regularity theory for fully nonlinear integro-differential equations. Commun. Pure Appl. Math. 62, 597–638 (2009)
4. Caffarelli, L., Silvestre, L.: Regularity results for nonlocal equations by approximation. Arch. Ration. Mech. Anal. 200, 59–88 (2011)
5. Caffarelli, L., Silvestre, L.: The Evans–Krylov theorem for nonlocal fully nonlinear equations. Ann. Math. 174, 1163–1187 (2011)
6. Evans, L.C.: Classical solutions of fully nonlinear, convex, second-order elliptic equations. Commun. Pure Appl. Math. 35, 333–363 (1982)
7. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. In: Grundlehren der Mathematischen Wissenschaften, vol. 224. Springer, Berlin (1977)
8. Jin, T., Xiong, J.: Schauder estimates for nonlocal fully nonlinear equations. Ann. de l’Institut Henri Poincare (C) Non Linear Anal. (2014) (in press)
9. Krylov, N.V.: Boundedly inhomogeneous elliptic and parabolic equations. Izv. Akad. Nauk SSSR Ser. Mat. 46, 487–523 (1982)
10. Kriventsov, D.: $$C^{1,\alpha }$$C1,α interior regularity for nonlocal elliptic equations with rough kernels. Commun. Partial Differ. Equ. 38, 2081–2106 (2013)
11. Ros-Oton, X., Serra, J.: Boundary regularity for fully nonlinear integro-differential equations (2014).arXiv:1404.1197
12. Ros-Oton, X., Serra, J.: Regularity theory for general stable operators (2014).arXiv:1412.3892
13. Serra, J.: Regularity for fully nonlinear nonlocal parabolic equation with rought kerenls (2012). doi:10.1007/s00526-014-0798-6
14. Silvestre, L.: Lecture notes on nonlocal equations (2014) (published online)
15. L. Silvestre and others, Nonlocal Equations Wiki. http://www.ma.utexas.edu/mediawiki