Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912505288196096 |
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| author | Bartolucci, Daniele Jevnikar, Aleks Wei, Juncheng Wu, Ruijun |
| author_facet | Bartolucci, Daniele Jevnikar, Aleks Wei, Juncheng Wu, Ruijun |
| contents | We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension $d=2$, under suitable natural integral bounds. It turns out that one of the asymptotic behaviors allowed corresponds to the Dancer-Yan spikes (J. London Math. Soc. ({\bf 78}) 2008, 639--662). Interestingly enough, roughly speaking and unlike the higher dimensional case, it is not true that any solution in the limit is a Dancer-Yan spike. Indeed, the spiking structure is more rich and we succeed in a detailed description of the singular behavior by a careful analysis, from local to global, of the tiny difference between the maximum value of the spikes and their ``vanishing level'' defining the free boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited Bartolucci, Daniele Jevnikar, Aleks Wei, Juncheng Wu, Ruijun Analysis of PDEs 35B40, 35B99, 35J61, 35J75, 35R35, 82D10 We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension $d=2$, under suitable natural integral bounds. It turns out that one of the asymptotic behaviors allowed corresponds to the Dancer-Yan spikes (J. London Math. Soc. ({\bf 78}) 2008, 639--662). Interestingly enough, roughly speaking and unlike the higher dimensional case, it is not true that any solution in the limit is a Dancer-Yan spike. Indeed, the spiking structure is more rich and we succeed in a detailed description of the singular behavior by a careful analysis, from local to global, of the tiny difference between the maximum value of the spikes and their ``vanishing level'' defining the free boundary. |
| title | Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited |
| topic | Analysis of PDEs 35B40, 35B99, 35J61, 35J75, 35R35, 82D10 |
| url | https://arxiv.org/abs/2507.20725 |