Gradient Estimates for Parabolic Systems from Composite Material

Haigang Li; Yanyan Li

Gradient Estimates for Parabolic Systems from Composite Material

Analysis of PDEs 2012-07-06 v2

Authors: Haigang Li , Yanyan Li

Abstract

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.

Keywords

gradient estimates parabolic partial differential equations special functions and series expansions

Cite

@article{arxiv.1105.1437,
  title  = {Gradient Estimates for Parabolic Systems from Composite Material},
  author = {Haigang Li and Yanyan Li},
  journal= {arXiv preprint arXiv:1105.1437},
  year   = {2012}
}

Comments

A new result is added which extends an $L^p$ estimate of Campanato for strongly parabolic systems to rather weak parabolic systems, see Appendix

Gradient Estimates for Parabolic Systems from Composite Material

Abstract

Keywords

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