The fractional Neumann and Robin type boundary conditions for the regional fractional <Emphasis Type="Italic">p</Emphasis>-Laplacian |
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Authors: | Mahamadi Warma |
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Institution: | 1.Department of Mathematics, College of Natural Sciences,University of Puerto Rico,San Juan,USA |
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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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