Lara, Héctor Chang; Dávila, Gonzalo \(C^{\sigma,\alpha}\) estimates for concave, non-local parabolic equations with critical drift. (English) Zbl 1353.35083 J. Integral Equations Appl. 28, No. 3, 373-394 (2016). Summary: Given a concave integro-differential operator \(I\), we study regularity for solutions of fully nonlinear, nonlocal, parabolic equations of the form \(u_t-Iu=0\). The kernels are assumed to be smooth but non necessarily symmetric, which accounts for a critical non-local drift. We prove a \(C^{\sigma +\alpha}\) estimate in the spatial variable and \(C^{1,\alpha}\) estimates in time assuming time regularity for the boundary data. The estimates are uniform in the order of the operator \(I\), hence allowing us to extend the classical Evans-Krylov result for concave parabolic equations. Cited in 6 Documents MSC: 35B45 A priori estimates in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs 35D40 Viscosity solutions to PDEs 35K55 Nonlinear parabolic equations 35R09 Integro-partial differential equations Keywords:fully nonlinear concave operators; Evans-Krylov estimate PDFBibTeX XMLCite \textit{H. C. Lara} and \textit{G. Dávila}, J. Integral Equations Appl. 28, No. 3, 373--394 (2016; Zbl 1353.35083) Full Text: DOI arXiv Euclid