论文标题
非本地诺伊曼问题的一般框架
A general framework for nonlocal Neumann problems
论文作者
论文摘要
在希尔伯特空间的框架内，我们解决了有界条件的有限域中的非局部问题。我们的主要重点是在相当普遍的环境中对不均匀的诺伊曼问题。我们还研究了从补体价值问题到本地边界价值问题的过渡。即使对于分数拉普拉斯操作员来说，几个结果也是新的。该设置还涵盖了Peridyanigics框架中的相关模型。
Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also study the transition from complement value problems to local boundary value problems. Several results are new even for the fractional Laplace operator. The setting also covers relevant models in the framework of peridynamics.
