On the existence of degenerate solutions of the two-dimensional $H$-system
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909327265103872 |
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| author | Guerra, André Lamy, Xavier Zemas, Konstantinos |
| author_facet | Guerra, André Lamy, Xavier Zemas, Konstantinos |
| contents | We consider entire solutions $ω\in\dot H^1(\mathbb R^2;\mathbb R^3)$ of the $H$-system $Δω=2ω_x\wedgeω_y,$ which we refer to as bubbles. Surprisingly, and contrary to conjectures raised in the literature, we find that bubbles with degree at least three can be degenerate: the linearized $H$-system around a bubble can admit solutions that are not tangent to the smooth family of bubbles. We then give a complete algebraic characterization of degenerate bubbles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the existence of degenerate solutions of the two-dimensional $H$-system Guerra, André Lamy, Xavier Zemas, Konstantinos Analysis of PDEs Differential Geometry We consider entire solutions $ω\in\dot H^1(\mathbb R^2;\mathbb R^3)$ of the $H$-system $Δω=2ω_x\wedgeω_y,$ which we refer to as bubbles. Surprisingly, and contrary to conjectures raised in the literature, we find that bubbles with degree at least three can be degenerate: the linearized $H$-system around a bubble can admit solutions that are not tangent to the smooth family of bubbles. We then give a complete algebraic characterization of degenerate bubbles. |
| title | On the existence of degenerate solutions of the two-dimensional $H$-system |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2409.18068 |