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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.10105 |
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| _version_ | 1866929244444033024 |
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| author | Lucà, Renato Merino, Pablo |
| author_facet | Lucà, Renato Merino, Pablo |
| contents | We consider the PDEs version of the Carleson problem in the context of the cubic nonlinear Klein-Gordon equation. This means that we aim to establish the lowest regularity class for which one has almost everywhere pointwise convergence of the solutions to the initial data, as $t \to 0$. We prove sharp results for initial data in Sobolev spaces and for their randomized counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pointwise convergence of the Klein-Gordon flow Lucà, Renato Merino, Pablo Analysis of PDEs 35L05, 35R60 We consider the PDEs version of the Carleson problem in the context of the cubic nonlinear Klein-Gordon equation. This means that we aim to establish the lowest regularity class for which one has almost everywhere pointwise convergence of the solutions to the initial data, as $t \to 0$. We prove sharp results for initial data in Sobolev spaces and for their randomized counterparts. |
| title | Pointwise convergence of the Klein-Gordon flow |
| topic | Analysis of PDEs 35L05, 35R60 |
| url | https://arxiv.org/abs/2402.10105 |