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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| Main Author: | |
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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 |
| Subjects: | |
| Online Access: | https://mathematicalanalysis.unibo.it/article/view/21056 |
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| Summary: | 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. |
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| ISSN: | 2240-2829 |