Equivalence of solutions to fractional \(p\)-Laplace type equations (Q2338116)

The article focuses on providing that some conceptions of a weak solution of the fractional \(p\)-Laplacian equation \[ \mathrm{P.V.} \int_{\mathbb{R}^n}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}dy=0. \] are equivalent. Precisely, on a bounded open set, the authors show that a superharmonic function is a viscosity supersolution, and vice versa.