We study a general version of the Cheeger inequality by considering the shape functional F-p,F-q(Omega) = lambda(1/p)(p)(Omega)/lambda q(1/q)(Omega). The infimum and the supremum of F-p,F-q are studied in the class of all domains Omega of R-d and in the subclass of convex domains. In the latter case the issue concerning the existence of an optimal domain for F-p,F-q is discussed.
On a class of Cheeger inequalities
Buttazzo, G;Prinari, F
2023-01-01
Abstract
We study a general version of the Cheeger inequality by considering the shape functional F-p,F-q(Omega) = lambda(1/p)(p)(Omega)/lambda q(1/q)(Omega). The infimum and the supremum of F-p,F-q are studied in the class of all domains Omega of R-d and in the subclass of convex domains. In the latter case the issue concerning the existence of an optimal domain for F-p,F-q is discussed.File in questo prodotto:
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