Stable domains for higher order elliptic operators

This paper is devoted to prove that any domain satisfying a \((\delta_0,r_0)-\)capacity condition of first order is automatically \((m,p)-\)stable for all \(m\geqslant 1\) and \(p\geqslant 1\), and for any dimension \(N\geqslant 1\). In particular, this includes regular enough domains such as \(\mathscr{C}^1-\)domains, Lipchitz domains, Reifenberg flat domains, but is weak enough to also includes cusp points. Our result extends some of the results of Hayouni and Pierre valid only for \(N=2,3\), and extends also the results of Bucur and Zolesio for higher order operators, with a different and simpler proof.