We investigate the stability of some inequalities of isoperimetric type related to Monge–Ampère functionals. In particular, firstly we prove the stability of a reverse Faber– Krahn inequality for the Monge–Ampère eigenvalue and its generalization. Then we give a stability result for the Brunn–Minkowski inequality and for a consequent Urysohn’s type inequality for the so-called n-torsional rigidity, a natural extension of the usual torsional rigidity.
Stability of isoperimetric type inequalities for some Monge–Ampère functionals
GHILLI, DARIA;
2014
Abstract
We investigate the stability of some inequalities of isoperimetric type related to Monge–Ampère functionals. In particular, firstly we prove the stability of a reverse Faber– Krahn inequality for the Monge–Ampère eigenvalue and its generalization. Then we give a stability result for the Brunn–Minkowski inequality and for a consequent Urysohn’s type inequality for the so-called n-torsional rigidity, a natural extension of the usual torsional rigidity.File in questo prodotto:
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