A Constructive Approach to a Class of Overdetermined Problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917354088169472 |
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| author | Fortunati, Alessandro Pacella, Filomena |
| author_facet | Fortunati, Alessandro Pacella, Filomena |
| contents | In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the celebrated Nekhoroshev Theorem. In a similar fashion to this class of results, we establish the existence of infinitely many approximants for the perturbed problem's solution, whose approximation error is so small which can be regarded as negligible for practical applications. The approach is fully constructive and this feature is demonstrated via an example in the final section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19446 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Constructive Approach to a Class of Overdetermined Problems Fortunati, Alessandro Pacella, Filomena Analysis of PDEs Functional Analysis Primary: 35N25, 35B20. Secondary: 35J25, 37J40 In this paper we study an overdetermined problem which is directly related to the well known torsion problem studied by J. Serrin. A perturbed version of the latter is tackled by using asymptotic series as well as tools borrowed from the celebrated Nekhoroshev Theorem. In a similar fashion to this class of results, we establish the existence of infinitely many approximants for the perturbed problem's solution, whose approximation error is so small which can be regarded as negligible for practical applications. The approach is fully constructive and this feature is demonstrated via an example in the final section. |
| title | A Constructive Approach to a Class of Overdetermined Problems |
| topic | Analysis of PDEs Functional Analysis Primary: 35N25, 35B20. Secondary: 35J25, 37J40 |
| url | https://arxiv.org/abs/2603.19446 |