Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics

We introduce new parametrized classes of shape admissible domains in $\mathbb{R}^n$, $n\geq 2$, and prove that they are compact with respect to the convergence sense characteristic functions, Hausdorff sense, compacts, weak their boundary volumes. The these bounded $(\varepsilon,\infty)$-domains possibly fractal boundaries can have parts any nonuniform dimension greater than or equal $n-1$ less $n$. existence optimal shapes such for maximum energy dissipation framework linear acoustics. A by-product our proof is result class fixed $\varepsilon$ stable under convergence. An additional related Mosco Robin-type functionals on converging domains.