Nonlinear fractional equations in the Heisenberg group
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Bologna
2024-01-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
| Subjects: | |
| Online Access: | https://mathematicalanalysis.unibo.it/article/view/18862 |
| _version_ | 1797359635310575616 |
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| author | Giampiero Palatucci Mirco Piccinini |
| author_facet | Giampiero Palatucci Mirco Piccinini |
| author_sort | Giampiero Palatucci |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T15:26:35Z |
| format | Article |
| id | doaj.art-8f606625fbe44c40a612ffb7071411f7 |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-03-08T15:26:35Z |
| publishDate | 2024-01-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-8f606625fbe44c40a612ffb7071411f72024-01-10T08:48:10ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292024-01-0114216320010.6092/issn.2240-2829/1886217224Nonlinear fractional equations in the Heisenberg groupGiampiero Palatucci0Mirco Piccinini1Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di ParmaDipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di ParmaWe 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.https://mathematicalanalysis.unibo.it/article/view/18862nonlocal operatorsfractional sublaplaciande~giorgi-nash-moser theoryheisenberg groupcaccioppoli estimatesobstacle problemsperron's method |
| spellingShingle | Giampiero Palatucci Mirco Piccinini Nonlinear fractional equations in the Heisenberg group Bruno Pini Mathematical Analysis Seminar nonlocal operators fractional sublaplacian de~giorgi-nash-moser theory heisenberg group caccioppoli estimates obstacle problems perron's method |
| title | Nonlinear fractional equations in the Heisenberg group |
| title_full | Nonlinear fractional equations in the Heisenberg group |
| title_fullStr | Nonlinear fractional equations in the Heisenberg group |
| title_full_unstemmed | Nonlinear fractional equations in the Heisenberg group |
| title_short | Nonlinear fractional equations in the Heisenberg group |
| title_sort | nonlinear fractional equations in the heisenberg group |
| topic | nonlocal operators fractional sublaplacian de~giorgi-nash-moser theory heisenberg group caccioppoli estimates obstacle problems perron's method |
| url | https://mathematicalanalysis.unibo.it/article/view/18862 |
| work_keys_str_mv | AT giampieropalatucci nonlinearfractionalequationsintheheisenberggroup AT mircopiccinini nonlinearfractionalequationsintheheisenberggroup |