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- Title
Nonlocal Harnack inequalities in the Heisenberg group.
- Authors
Palatucci, Giampiero; Piccinini, Mirco
- Abstract
We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group H n , whose prototype is the Dirichlet problem for the p-fractional subLaplace equation. These problems arise in many different contexts in quantum mechanics, in ferromagnetic analysis, in phase transition problems, in image segmentations models, and so on, when non-Euclidean geometry frameworks and nonlocal long-range interactions do naturally occur. We prove general Harnack inequalities for the related weak solutions. Also, in the case when the growth exponent is p = 2 , we investigate the asymptotic behavior of the fractional subLaplacian operator, and the robustness of the aforementioned Harnack estimates as the differentiability exponent s goes to 1.
- Subjects
DIRICHLET problem; NON-Euclidean geometry; IMAGE segmentation; NONLINEAR equations; QUANTUM mechanics; PHASE space
- Publication
Calculus of Variations & Partial Differential Equations, 2022, Vol 61, Issue 5, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-022-02301-9