摘要
In this paper, we derive W^(1,∞) and piecewise C^(1,α) estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56:892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.
In this paper, we derive W^（1,∞） and piecewise C^（1,α） estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise H¨older continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56：892–925] on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11571042, 11371060 and 11631002)
Fok Ying Tung Education Foundation (Grant No. 151003)
National Science Foundation of USA (Grant No. DMS-0701545)
