A regularized penalty-multiplier method for approximating cavitation solutions with prescribed cavity volume size

Pablo V. Negrón-Marrero, Jeyabal Sivaloganathan

Let $\Omega \in {\mathbb{R}}^n$ be the region occupied by a body and let ${\mathbf{x}}_0$ be a flaw point in $\Omega$. Let $E(\cdot )$ be an energy functional (defined on some appropriate admissibl…