Abstract
AbstractWe show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.
Funder
Johann Wolfgang Goethe-Universität, Frankfurt am Main
Publisher
Springer Science and Business Media LLC
Reference5 articles.
1. Abatangelo, N., Valdinoci, E.: Getting acquainted with the fractional Laplacian. In: Contemporary Research in Elliptic PDEs and Related Topics, Springer INdAM Ser., vol. 33, pp. 1–105. Springer, Cham (2019)
2. Bogdan, K., Burdzy, K., Chen, Z.-Q.: Censored stable processes. Probab. Theory Related Fields 127(1), 89–152 (2003)
3. Chen, Z.-Q., Kumagai, T.: Heat kernel estimates for stable-like processes on d-sets. Stochastic Process. Appl. 108(1), 27–62 (2003)
4. Dipierro, S., Ros-Oton, X., Valdinoci, E.: Nonlocal problems with Neumann boundary conditions. Rev. Mat. Iberoam. 33(2), 377–416 (2017)
5. Leonori, T., Medina, M., Peral, I., Primo, A., Soria, F.: Principal eigenvalue of mixed problem for the fractional Laplacian: moving the boundary condition. J. Differential Equations 265(2), 593–619 (2018)
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献