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Parabolic Systems with Polynomial Growth and Regularity

Frank DuzaarGiuseppe MingioneKlaus Steffen

出版	American Mathematical Soc., 2011
主題	Mathematics / Algebra / GeneralMathematics / Differential Equations / GeneralMathematics / Differential Equations / Partial
ISBN	08218496709780821849675
URL	http://books.google.com.hk/books?id=zD_VAwAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.