A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems

摘要: We prove partial regularity for minimizers to elasticity type energies in the nonlinear framework {with $p$-growth, $p>1$,} dimension $n\geq 3$. It is an open problem such a setting either establish full or provide counterexamples. In particular, we give estimate on Hausdorff of potential singular set by proving that strictly less than {$n-(p^*\wedge 2)$, and actually $n-2$ autonomous case} (full well-known $2$). The latter result instrumental existence strong formulation Griffith models brittle fracture with constitutive relations, accounting damage plasticity space dimensions $2$ $3$.