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Author: Valdinoci, Enrico × End date: 2019 × Start date: 2019 × Type: Text × Subject: fractional operators ×

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Now showing 1 - 3 of 3
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    Homogenization and Orowan's law for anisotropic fractional operators of any order
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Patrizi, Stefania; Valdinoci, Enrico
    We consider an anisotropic Lévy operator Is of any order s 2 (0, 1) and we consider the homogenization properties of an evolution equation. The scaling properties and the effective Hamiltonian that we obtain is different according to the cases s < 1/2 and s > 1/2. In the isotropic onedimensional case, we also prove a statement related to the so-called Orowans law, that is an appropriate scaling of the effective Hamiltonian presents a linear behavior.
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    Chaotic orbits for systems of nonlocal equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dipierro, Serena; Patrizi, Stefania; Valdinoci, Enrico
    We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic trajectories are constructed. This is the first attempt to consider a nonlocal version of this type of dynamical systems in a variational setting and the first result regarding symbolic dynamics in a fractional framework.
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    Continuity and density results for a one-phase nonlocal free boundary problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dipierro, Serena; Valdinoci, Enrico
    We consider a one-phase nonlocal free boundary problem obtained by the superposition of a fractional Dirichlet energy plus a nonlocal perimeter functional. We prove that the minimizers are Hölder continuous and the free boundary has positive density from both sides. For this, we also introduce a new notion of fractional harmonic replacement in the extended variables and we study its basic properties.