\(C^{1,\alpha}\) interior regularity for nonlinear nonlocal elliptic equations with rough kernels. (English) Zbl 1281.35092
Summary: We prove a \(C^{1,\alpha}\) interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity of a special class of nonlinear operators.
MSC:
35R09 | Integro-partial differential equations |
35R11 | Fractional partial differential equations |
45K05 | Integro-partial differential equations |
47G20 | Integro-differential operators |
35B65 | Smoothness and regularity of solutions to PDEs |
References:
[1] | DOI: 10.1016/j.anihpc.2007.02.007 · Zbl 1155.45004 · doi:10.1016/j.anihpc.2007.02.007 |
[2] | Barrios B., Ann. Scuola Norm. Sup. Pisa Cl. Sci. |
[3] | DOI: 10.1016/j.jfa.2009.05.012 · Zbl 1177.45013 · doi:10.1016/j.jfa.2009.05.012 |
[4] | Caffarelli L., Fully Nonlinear Elliptic Equations 43 (1995) · Zbl 0834.35002 · doi:10.1090/coll/043 |
[5] | DOI: 10.1002/cpa.20274 · Zbl 1170.45006 · doi:10.1002/cpa.20274 |
[6] | DOI: 10.4007/annals.2011.174.2.9 · Zbl 1232.49043 · doi:10.4007/annals.2011.174.2.9 |
[7] | DOI: 10.1007/s00205-010-0336-4 · Zbl 1231.35284 · doi:10.1007/s00205-010-0336-4 |
[8] | DOI: 10.3934/dcds.2013.33.2319 · Zbl 1263.45008 · doi:10.3934/dcds.2013.33.2319 |
[9] | DOI: 10.1007/BF00281780 · Zbl 0708.35019 · doi:10.1007/BF00281780 |
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