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    • On a class of Cheeger inequalities
    Authors: Luca, Briani; Giuseppe, Buttazzo; Francesca, Prinari;  Advisor: -;  Co-Author: - (2022)

    We study a general version of the Cheeger inequality by considering the shape functional Fp,q(Ω)=λ1/pp(Ω)/λ1/qq(Ω). The infimum and the supremum of Fp,q are studied in the class of all domains Ω of Rd and in the subclass of convex domains. In the latter case the issue concerning the existence of an optimal domain for Fp,q is discussed.