  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.
