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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.07251 |
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| _version_ | 1866910113386725376 |
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| author | Jiechen, Qiang Zhongwei, Tang Yichen, Zhang Ning, Zhou |
| author_facet | Jiechen, Qiang Zhongwei, Tang Yichen, Zhang Ning, Zhou |
| contents | In this paper, we investigate the compactness of nonnegative solutions to a critical sub-elliptic equation with a nonnegative potential on the Heisenberg group. We establish that the solution set is compact provided the potential satisfies certain non-degeneracy conditions. Moreover, we show that if a sequence of solutions blows up, both the potential and its sub-Laplacian must vanish at the blow-up point. Our analysis overcomes the inherent geometric and analytical challenges posed by the Heisenberg group, including the degeneracy of the sub-Laplacian, its non-commutative structure, and the anisotropic dilation symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07251 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compactness of Solutions to Sub-Elliptic Equations with Potential on the Heisenberg Group Jiechen, Qiang Zhongwei, Tang Yichen, Zhang Ning, Zhou Analysis of PDEs In this paper, we investigate the compactness of nonnegative solutions to a critical sub-elliptic equation with a nonnegative potential on the Heisenberg group. We establish that the solution set is compact provided the potential satisfies certain non-degeneracy conditions. Moreover, we show that if a sequence of solutions blows up, both the potential and its sub-Laplacian must vanish at the blow-up point. Our analysis overcomes the inherent geometric and analytical challenges posed by the Heisenberg group, including the degeneracy of the sub-Laplacian, its non-commutative structure, and the anisotropic dilation symmetry. |
| title | Compactness of Solutions to Sub-Elliptic Equations with Potential on the Heisenberg Group |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.07251 |