Some evaluations of the fractional p-Laplace operator on radial functions

We face a rigidity problem for the fractional p-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that (-Delta)(s)(1 - vertical bar x vertical bar(2))(+)(s) and -Delta(p)(1 - vertical bar x vertical bar(p/p-1)) are constant functions in (-1, 1) for fixed p and s. We evaluated (-Delta(p))(s)(1 - vertical bar x vertical bar(p/p-1))(+)(s) proving that it is not constant in (-1, 1) for some p is an element of (1, +infinity) and s is an element of (0, 1). This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas.