Evolution driven by the infinity fractional Laplacian
Peer reviewed, Journal article
Published version
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https://hdl.handle.net/11250/3104950Utgivelsesdato
2023Metadata
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- Institutt for matematiske fag [2486]
- Publikasjoner fra CRIStin - NTNU [38484]
Originalversjon
Calculus of Variations and Partial Differential Equations. 2023, 62 (4), 1-30. 10.1007/s00526-023-02475-wSammendrag
We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland et al. (Adv Math 230(4–6):1859–1894, 2012) as the infinitesimal generator of a non-Brownian tug-of-war game. We first construct a class of viscosity solutions of the initial-value problem for bounded and uniformly continuous data. An important result is the equivalence of the nonlinear operator in higher dimensions with the one-dimensional fractional Laplacian when it is applied to radially symmetric and monotone functions. Thanks to this and a comparison theorem between classical and viscosity solutions, we are able to establish a global Harnack inequality that, in particular, explains the long-time behavior of the solutions.