Energy estimates and cavity interaction for a critical-exponent cavitation model

Duvan Henao, Sylvia Serfaty

We consider the minimization of $\int_{Ω_{\ep}} |D\vec u|^p \dd\vec x$ in a perforated domain $Ω_{\ep}:= Ω\setminus \bigcup_{i=1}^M B_{\ep}(\vec a_i)$ of ${\mathbb{R}}^n$, among maps $\vec u…