# Parabolic Systems with Polynomial Growth and Regularity

## (Memoirs of the American Mathematical Society, 214)

 Author Frank Duzaar Isbn 9780821849675 File size 967.71KB Year 2011 Pages 118 Language English File format PDF Category Mathematics

### Book 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.