On the Convergence of a Regularization Scheme for Approximating Cavitation Solutions with Prescribed Cavity Volume

Let \Omega\in\mathbb{R}^n n=2,3 be the region occupied by a hyperelastic body in its reference configuration. Let E(\cdot)be the stored energy functional, and let x_0be a flaw point in \Omega(i.e., a point of possible discontinuity for admissible deformations of the body). For V>0fixed, let u_Vbe a minimizer of E(\cdot)among the set of discontinuous deformations uconstrained to form a hole of prescribed volume Vat...