Work

Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition

Year: 2024

Type: article

Abstract: In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of C1,1-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 [Cantarella et al., 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 C1,1-domains for a first curl eigenvalue problem which has been studied recently for other classes of domains in [Enciso et al., Trans. Am. Math. Soc. 377, 4519–4540 (2024)].

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0163183

Author: Wadim Gerner

Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Sorbonne Université, Laboratoire Jacques-Louis Lions

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Institut national de recherche en informatique et en automatique (INRIA)

OpenAlex ID: W4401585496