Parabolic Systems with Polynomial Growth and Regularity

(Memoirs of the American Mathematical Society, 214)

5bf5fc3f20bb9.jpg 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.



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