Nonlinear fractional equations in the Heisenberg group

Authors

  • Giampiero Palatucci Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma
  • Mirco Piccinini Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma

DOI:

https://doi.org/10.6092/issn.2240-2829/18862

Keywords:

nonlocal operators, fractional subLaplacian, De~Giorgi-Nash-Moser theory, Heisenberg group, Caccioppoli estimates, obstacle problems, Perron's method

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,∞) and differentiability order 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.

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Published

2024-01-09

How to Cite

Palatucci, G., & Piccinini, M. (2023). Nonlinear fractional equations in the Heisenberg group. Bruno Pini Mathematical Analysis Seminar, 14(2), 163–200. https://doi.org/10.6092/issn.2240-2829/18862

Issue

Vol. 14 No. 2 (2023): Seminars 2023

Section

Articles

License

Copyright (c) 2024 Mirco Piccinini, Giampiero Palatucci

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 Unported License.