Some shape functionals for the k-Hessian equation
Abstract
For a non-empty, bounded, open, and convex set of class C2, we consider the Torsional Rigidity associated to the k-Hessian operator. We first prove P\'olya type lower bound for the k-Torsional Rigidity in any dimension; then, in order to investigate optimal sets in the P\'olya type inequality, we provide two quantitative estimates.
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