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 6002018&_mathId=si2.gif&_user=111111111&_pii=S0022247X16002018&_rdoc=1&_issn=0022247X&md5=04ec35fa9aed5457992757dcc04162e5">6002018-si2.gif">$\frac{2n}{n+2}<p<2$. The inhomogeneity B satisfies the controllable growth condition where 6002018&_mathId=si4.gif&_user=111111111&_pii=S0022247X16002018&_rdoc=1&_issn=0022247X&md5=21635fd515747cfc843d0866e196aeaa">6002018-si4.gif">$p^{⁎}=\frac{(n+2)p}{n+2-p}$, if 6002018&_mathId=si5.gif&_user=111111111&_pii=S0022247X16002018&_rdoc=1&_issn=0022247X&md5=cce4e6e7c4d4c312005da4eacc969d6c" title="Click to view the MathML source">n+2≠p$n+2\ne p$. Here 6002018&_mathId=si6.gif&_user=111111111&_pii=S0022247X16002018&_rdoc=1&_issn=0022247X&md5=b8fbda977868c5e3705944edde83023b" title="Click to view the MathML source">p^⁎$p^{⁎}$ can be any exponent if 6002018&_mathId=si7.gif&_user=111111111&_pii=S0022247X16002018&_rdoc=1&_issn=0022247X&md5=fa93e2d0d0bc5b1c8d58cd0fdfabf7bf" title="Click to view the MathML source">n+2=p$n+2=p$. The proof is based on the 6002018&_mathId=si113.gif&_user=111111111&_pii=S0022247X16002018&_rdoc=1&_issn=0022247X&md5=e724274eac5ad96efacc2da56bc72846" title="Click to view the MathML source">A$\mathcal{A}$-caloric approximation lemma to parabolic systems with subquadratic growth.