Symmetry problems for gauge balls in the Heisenberg group
In this note we focus on possible characterizations of gauge-symmetric functions in the Heisenberg group. We discuss a family of inverse problems in potential theory relating solid and surface weighted mean-value formulas, and we show a partial solution to such problems. To this aim, we review a uni...
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| Format: | Article |
| Language: | English |
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University of Bologna
2025-01-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | https://mathematicalanalysis.unibo.it/article/view/21056 |
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| author | Giulio Tralli |
| author_facet | Giulio Tralli |
| author_sort | Giulio Tralli |
| collection | DOAJ |
| description | In this note we focus on possible characterizations of gauge-symmetric functions in the Heisenberg group. We discuss a family of inverse problems in potential theory relating solid and surface weighted mean-value formulas, and we show a partial solution to such problems. To this aim, we review a uniqueness result for gauge balls obtained with V. Martino in [23] by means of overdetermined problems of Serrin-type. The class of competitor sets we consider enjoys partial symmetries of toric and cylindrical type. |
| format | Article |
| id | doaj-art-fc59e54efb2b4a77b6a6795a58f08192 |
| institution | Kabale University |
| issn | 2240-2829 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj-art-fc59e54efb2b4a77b6a6795a58f081922025-01-15T16:52:44ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292025-01-01151799710.6092/issn.2240-2829/2105619430Symmetry problems for gauge balls in the Heisenberg groupGiulio Tralli0Dipartimento di Matematica e Informatica, Università di FerraraIn this note we focus on possible characterizations of gauge-symmetric functions in the Heisenberg group. We discuss a family of inverse problems in potential theory relating solid and surface weighted mean-value formulas, and we show a partial solution to such problems. To this aim, we review a uniqueness result for gauge balls obtained with V. Martino in [23] by means of overdetermined problems of Serrin-type. The class of competitor sets we consider enjoys partial symmetries of toric and cylindrical type.https://mathematicalanalysis.unibo.it/article/view/21056heisenberg sublaplacianinverse problems in potential theoryoverdetermined problems |
| spellingShingle | Giulio Tralli Symmetry problems for gauge balls in the Heisenberg group Bruno Pini Mathematical Analysis Seminar heisenberg sublaplacian inverse problems in potential theory overdetermined problems |
| title | Symmetry problems for gauge balls in the Heisenberg group |
| title_full | Symmetry problems for gauge balls in the Heisenberg group |
| title_fullStr | Symmetry problems for gauge balls in the Heisenberg group |
| title_full_unstemmed | Symmetry problems for gauge balls in the Heisenberg group |
| title_short | Symmetry problems for gauge balls in the Heisenberg group |
| title_sort | symmetry problems for gauge balls in the heisenberg group |
| topic | heisenberg sublaplacian inverse problems in potential theory overdetermined problems |
| url | https://mathematicalanalysis.unibo.it/article/view/21056 |
| work_keys_str_mv | AT giuliotralli symmetryproblemsforgaugeballsintheheisenberggroup |