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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.16763 |
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| _version_ | 1866910680900173824 |
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| author | Palatucci, Giampiero Piccinini, Mirco |
| author_facet | Palatucci, Giampiero Piccinini, Mirco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16763 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlinear fractional equations in the Heisenberg group Palatucci, Giampiero Piccinini, Mirco Analysis of PDEs 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. |
| title | Nonlinear fractional equations in the Heisenberg group |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.16763 |