Symmetrization for fractional Neumann problems

详细信息    查看全文

• 作者：Bruno Volzone ^{bruno.volzone@uniparthenope.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B45 ; 35R11 ; 35K20
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：147
• 期：Complete
• 页码：1-25
• 全文大小：768 K

文摘

In this paper we complement the program concerning the application of symmetrization methods to nonlocal PDEs by providing new estimates, in the sense of mass concentration comparison, for solutions to linear fractional elliptic and parabolic PDEs with Neumann boundary conditions. These results are achieved by employing suitable symmetrization arguments to the Stinga–Torrea local extension problems, corresponding to the fractional boundary value problems considered. Sharp estimates are obtained first for elliptic equations and a certain number of consequences in terms of regularity estimates is then established. Finally, a parabolic symmetrization result is covered as an application of the elliptic concentration estimates in the implicit time discretization scheme.