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 (-Δ)^s(1 - |x|^2)^s_+ and -Δp(1 - |x|^(p/p-1) ) are constant functions in (-1; 1) for fixed p and s. We evaluated (-Δp)_s(1 - |x|^(p/p-1) )^s_+ proving that it is not constant in (-1; 1) for some p in (1; infty) and s in (0; 1). This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas.
Some evaluations of the fractional p-Laplace operator on radial functionsy
Gervasio P.;Quarteroni A.
2022-01-01
Abstract
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 (-Δ)^s(1 - |x|^2)^s_+ and -Δp(1 - |x|^(p/p-1) ) are constant functions in (-1; 1) for fixed p and s. We evaluated (-Δp)_s(1 - |x|^(p/p-1) )^s_+ proving that it is not constant in (-1; 1) for some p in (1; infty) and s in (0; 1). This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas.File in questo prodotto:
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