Partial regularity for subquadratic parabolic systems under controllable growth conditions

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• 作者：Yichen Dai^a ; ^{yichendai0613@163.com" class="auth_mail" title="E-mail the corresponding author} ; Zhong Tan^b ; ¹ ; ^{tan85@xmu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Shuhong Chen^c ; ² ; ^{shiny0320@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Subquadratic parabolic systems ; Controllable growth condition ; Partial regularity ; AA-caloric approximation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：439
• 期：2
• 页码：481-513
• 全文大小：534 K

文摘

In this paper, we prove a regularity result for weak solutions away from singular set of parabolic systems with subquadratic growth condition of the type where the structure function a   satisfies standard ellipticity and growth condition with polynomial growth rate $\frac{2n}{n+2}<p<2$. The inhomogeneity B satisfies the controllable growth condition where $p^{⁎}=\frac{(n+2)p}{n+2\&<font\; color="red">min</font>us;p}$, if n+2≠p$n+2\ne p$. Here p^⁎$p^{⁎}$ can be any exponent if n+2=p$n+2=p$. The proof is based on the A$\mathcal{A}$-caloric approximation lemma to parabolic systems with subquadratic growth.