We consider shape functionals of the form $F_q(Omega)=P(Omega)T^q(Omega)$ on the class of open sets of prescribed Lebesgue measure. Here $q>0$ is fixed, $P(Omega)$ denotes the perimeter of $Omega$ and $T(Omega)$ is the torsional rigidity of $Omega$. The minimization and maximization of $F_q(Omega)$ is considered on various classes of admissible domains $Omega$: in the class ${cal A}_{all}$ of {it all domains}, in the class ${cal A}_{convex}$ of {it convex domains}, and in the class ${cal A}_{thin}$ of {it thin domains}.

Some inequalities involving perimeter and torsional rigidity

Giuseppe Buttazzo
;
Francesca Prinari
2021-01-01

Abstract

We consider shape functionals of the form $F_q(Omega)=P(Omega)T^q(Omega)$ on the class of open sets of prescribed Lebesgue measure. Here $q>0$ is fixed, $P(Omega)$ denotes the perimeter of $Omega$ and $T(Omega)$ is the torsional rigidity of $Omega$. The minimization and maximization of $F_q(Omega)$ is considered on various classes of admissible domains $Omega$: in the class ${cal A}_{all}$ of {it all domains}, in the class ${cal A}_{convex}$ of {it convex domains}, and in the class ${cal A}_{thin}$ of {it thin domains}.
2021
Briani, Luca; Buttazzo, Giuseppe; Prinari, FRANCESCA AGNESE
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1075725
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 10
social impact