Neumann conditions for the higher order $s$-fractional Laplacian $(-\Delta {)}^{s}u$ with $s>1$

Abstract

In this paper we study a variational Neumann problem for the higher order $s$-fractional Laplacian, with $s>1$. In the process, we introduce some non-local Neumann boundary conditions that appear in a natural way from a Gauss-like integration formula.