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 $\mathscr{C}^1-$...
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| creator | Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2307.07217 |
| format | Article |
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$(\delta_0,r_0)-$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
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$(\delta_0,r_0)-$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
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$(\delta_0,r_0)-$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.</abstract><doi>10.48550/arxiv.2307.07217</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics Mathematics - Optimization and Control |
| title | Stable domains for higher order elliptic operators |
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