Lorentz estimates for fully nonlinear parabolic and elliptic equations

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• 作者：Junjie Zhang ^{junjiezhang@bjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Shenzhou Zheng ; ^{shzhzheng@bjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35D35 ; 35J60 ; 35K55
• 刊名：Nonlinear Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：148
• 期：Complete
• 页码：106-125
• 全文大小：733 K

文摘

We prove an interior Lorentz estimate of the Hessian of strong solutions to fully nonlinear parabolic equations and elliptic equations F(D²u,x)=f(x)$F(D^{2}u,x)=f\left(x\right)$, respectively. Here, we assume that the associated nonlinearities satisfy uniformly parabolic condition or ellipticity, certain growth condition and the (δ,R)$(\delta ,R)$-vanishing condition. We establish Lorentz estimates for such fully nonlinear equations based on the approach of the large-35809d1b3359f9936" title="Click to view the MathML source">M$M$-inequality principle introduced by Acerbi–Mingione.