Preprint

Inserted: 13 jul 2023
Last Updated: 16 feb 2024

Year: 2023

Abstract:

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 partially extends also the results of Bucur and Zolesio for higher order operators, with a different and simpler proof.

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