Asymptotic analysis of Dirichlet problems in supercritically perforated domains via quantification by torsional rigidity

We study the Dirichlet problem $-\mathrm{div}(A^{\varepsilon}\nabla u^{\varepsilon}) = f$ on varying open sets $D^{\varepsilon}$, with uniformly elliptic coefficients $A^{\varepsilon}$, in the regime where the solutions vanish in the limit for every source. For periodically perforated domains, this