Abstract
Let \({p \in (1,\infty)}\), \({s \in (0,1)}\) and \({\Omega \subset {\mathbb{R}^{N}}}\) a bounded open set with boundary \({\partial\Omega}\) of class C 1,1. In the first part of the article we prove an integration by parts formula for the fractional p-Laplace operator \({(-\Delta)_{p}^{s}}\) defined on \({\Omega \subset {\mathbb{R}^{N}}}\) and acting on functions that do not necessarily vanish at the boundary \({\partial\Omega}\). In the second part of the article we use the above mentioned integration by parts formula to clarify the fractional Neumann and Robin boundary conditions associated with the fractional p-Laplacian on open sets.
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Warma, M. The fractional Neumann and Robin type boundary conditions for the regional fractional p-Laplacian. Nonlinear Differ. Equ. Appl. 23, 1 (2016). https://doi.org/10.1007/s00030-016-0354-5
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DOI: https://doi.org/10.1007/s00030-016-0354-5