Three representations of the fractional p-Laplacian: Semigroup, extension and Balakrishnan formulas - del Teso, F; Gómez-Castro, D; Vázquez, JL (De Gruyter, 2021)
We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity with the linear heat semigroup. The second adapts the nonlinearity to the Caffarelli-Silvestre linear extension technique. The third one is the corresponding nonlinear version of the Balakrishnan formula. We also discuss the correct choice of the constant of the fractional p-Laplace operator in order to have continuous dependence as p → 2 and s → 0+, 1−.