Gradient Estimates for Parabolic Systems from Composite Material

Details Gradient Estimates for Parabolic Systems from Composite Material Gradient Estimates for Parabolic Systems from Composite Material

2011-05-07

arxiv.org/abs/1105.1437v1

Mathematics

Analysis of PDEs

45 pages

Scientific paper

In this paper we derive $W^{1,\infty}$ and piecewise $C^{1,\alpha}$ 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 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.

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