Nonlocal Harnack inequalities in the Heisenberg group

Abstract We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group $$\mathbb {H}^n$$ Hn , whose prototype is Dirichlet problem for p -fractional subLaplace equation. These arise many different contexts quantum mechanics, ferromagnetic analysis, phase transition problems, image segmentations models, and so on, when non-Euclidean geometry frameworks nonlocal long-range interactions do naturally occur. prove general Harnack inequalities related weak solutions. Also, case growth exponent $$p=2$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">p=2 we investigate asymptotic behavior fractional subLaplacian operator, robustness aforementioned estimates as differentiability s goes to 1.