Vol. 11, No. 6, 2018

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Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts

Hongjie Dong, Tianling Jin and Hong Zhang

Vol. 11 (2018), No. 6, 1487–1534
Abstract

We obtain Dini- and Schauder-type estimates for concave fully nonlinear nonlocal parabolic equations of order σ (0,2) with rough and nonsymmetric kernels and drift terms. We also study such linear equations with only measurable coefficients in the time variable, and obtain Dini-type estimates in the spacial variable. This is a continuation of work by the authors Dong and Zhang.

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Keywords
nonlocal fully nonlinear parabolic equations, Dini- and Schauder-type estimates, critical drift terms
Mathematical Subject Classification 2010
Primary: 35B45, 35K55, 35R09
Secondary: 35B65, 60J75
Milestones
Received: 30 September 2017
Revised: 14 January 2018
Accepted: 14 February 2018
Published: 3 May 2018
Authors
Hongjie Dong
Division of Applied Mathematics
Brown University
Providence, RI
United States
Tianling Jin
Department of Mathematics
The Hong Kong University of Science and Technology
Kowloon
Hong Kong
Hong Zhang
Division of Applied Mathematics
Brown University
Providence, RI
United States