Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition
| Autor: | Gerner, Wadim |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of $C^{1,1}$-regular domains satisfying a uniform ball condition as long as the desired objective function satisfies certain properties. We then verify that the helicity isoperimetric problem studied in [J. Cantarella, D. DeTurck, H. Gluck and M. Teytel, J. Math. Phys. 41, 5615 (2000)] satisfies the conditions of our framework and hence establish the existence of optimal domains within the given class of domains. We additionally use the same framework to prove the existence of optimal domains among uniform $C^{1,1}$-domains for a first curl eigenvalue problem which has been studied recently for other classes of domains in [A. Enciso, W. Gerner and D. Peralta-Salas, Trans. Amer. Math. Soc. 377, 4519-4540 (2024)]. Comment: 15 pages; A gap in the proof of one of the applications of the main theorem in Corollary 2.7 has been filled. To this end, a more general version of the original Theorem 2.6 has been established in this version. The following article has been accepted by Journal of Mathematical Phyiscs. After it is published, it will be found at https://pubs.aip.org/aip/jmp |
| Databáze: | arXiv |
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