A priori estimates and application to the symmetry of solutions for critical p-Laplace equations

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• 作者：Jé ; rô ; me Vé ; tois ^{jerome.vetois@mcgill.ca" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 January 2016
• 年：2016
• 卷：260
• 期：1
• 页码：149-161
• 全文大小：302 K

文摘

We establish pointwise a priori estimates for solutions in 782c50af489" title="Click to view the MathML source">D^1,p(Rⁿ)$D^{1,p}\left({\mathbb{R}}^n\right)$ of equations of type −螖_pu=f(x,u)$-{\mathrm{螖}}_{p}u=f(x,u)$, where p∈(1,n)$p\in (1,n)$, 螖_p:=div(|∇u|^p−2∇u)${\mathrm{螖}}_p:=\mathrm{div}\left({\left|\mathrm{\nabla }u\right|}^{p-2}\mathrm{\nabla }u\right)$ is the p-Laplace operator, and f is a Caratheodory function with critical Sobolev growth. In the case of positive solutions, our estimates allow us to extend previous radial symmetry results. In particular, by combining our results and a result of Damascelli–Ramaswamy [6], we are able to extend a recent result of Damascelli–Merchán–Montoro–Sciunzi [7] on the symmetry of positive solutions in 782c50af489" title="Click to view the MathML source">D^1,p(Rⁿ)$D^{1,p}\left({\mathbb{R}}^n\right)$ of the equation e7dccfcd2d8c5107" title="Click to view the MathML source">−螖_pu=u^{p鈦?/sup>−1}$-{\mathrm{螖}}_{p}u=u^{p^{鈦?/mo>}-1}$, where p^{鈦?/sup>:=np/(n−p)}$p^{鈦?/mo>}:=np/(n-p)$.