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- W3193999072 abstract "We introduce three representation formulas for the fractional $p$-Laplace operator in the whole range of parameters $0<s<1$ and $1<p<infty$. Note that for $pne 2$ 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 $pto 2$ and $s to 0^+, 1^-$. 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 $W^{s,p}(mathbb{R}^n)$ seminorms." @default.
- W3193999072 created "2021-08-30" @default.
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- W3193999072 date "2021-08-01" @default.
- W3193999072 modified "2023-09-30" @default.
- W3193999072 title "Three Representations of the Fractional p-Laplacian: Semigroup, Extension and Balakrishnan Formulas" @default.
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- W3193999072 doi "https://doi.org/10.1515/fca-2021-0042" @default.
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