\(C^{1,\alpha}\) 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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
