Published Paper
Inserted: 27 apr 2023
Last Updated: 1 mar 2024
Journal: Bruno Pini Math. Anal. Semin.
Year: 2024
Abstract:
We deal with a wide class of nonlinear nonlocal equations led by integro-differential operators of order $(s,p)$, with summability exponent $p \in (1,\infty)$ and differentiability exponent $s\in (0,1)$, whose prototype is the fractional subLaplacian in the Heisenberg group. We present very recent boundedness and regularity estimates (up to the boundary) for the involved weak solutions, and we introduce the nonlocal counterpart of the Perron Method in the Heisenberg group, by recalling some results on the fractional obstacle problem. Throughout the paper we also list various related open problems
Keywords: Heisenberg group, obstacle problems, Caccioppoli estimates, Nonlocal operators, fractional subLaplacian, De Giorgi-Nash-Moser theory, Perron's method
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