Parabolic systems with polynomial growth and regularity
Author(s)
Bibliographic Information
Parabolic systems with polynomial growth and regularity
（Memoirs of the American Mathematical Society, no. 1005）
American Mathematical Society, c2011
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"November 2011, volume 214, number 1005 (first of 5 numbers )."
Includes bibliography (p. 115-118)
Description and Table of Contents
Description
The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $|a(x,t,u,Du)|\leq L(1+|Du|^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.
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