A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909165533790208 |
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| author | Martinez-Baena, J. Silverio Villegas, Salvador |
| author_facet | Martinez-Baena, J. Silverio Villegas, Salvador |
| contents | In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse index solutions. We provide a negative answer showing the existence of sequences of solutions with radial Morse index equal to 1 for which regularity estimates can not be satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems Martinez-Baena, J. Silverio Villegas, Salvador Analysis of PDEs 42B37, 46E35 In the regularity theory of solutions to elliptic partial differential equations often the concept of stability plays the role of a sufficient condition for smoothness. It is a natural question to ask if this holds true for nonstable but finite Morse index solutions. We provide a negative answer showing the existence of sequences of solutions with radial Morse index equal to 1 for which regularity estimates can not be satisfied. |
| title | A negative result on regularity estimates on finite radial Morse index solutions to elliptic problems |
| topic | Analysis of PDEs 42B37, 46E35 |
| url | https://arxiv.org/abs/2404.06944 |