Gradient estimates for parabolic systems from composite material

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（11）
• 页码范围: 2011-2052
• 页数: 42页
• 语种: 英文
• DOI: 10.1007/s11425-017-9153-0

摘要

In this paper,we derive W1,∞ and piecewise C1,α estimates for solutions,and their t-derivatives,of divergence form parabolic systems with coefficients piecewise H(o)lder 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.