Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas

We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 A number of consequences and proposals are derived. Thus, we propose a natural spectral-type operator in domains, different from the standard restriction of the fractional p-Laplace operator acting on the whole space. We also propose numerical schemes, a new definition of the fractional p-Laplacian on manifolds, as well as alternative characterizations of the Ws, p(ℝn) seminorms.