  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)].
