A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity

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• 作者：Hui Yu ^{hyu@math.utexas.edu}
• 关键词：Nonlocal elliptic equations ; Degenerate elliptic equations ; Higher regularity ; Dirichlet problem ; Diffusion process
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：326-346
• 全文大小：376 K
• 卷排序：448

文摘

We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the viscosity sense. If we further assume uniform ellipticity then the solution is shown to be classical, and even smooth if both the operator and the boundary datum are smooth.