Abstract
AbstractWe provide a novel approach to approximate bounded Lipschitz domains via a sequence of smooth, bounded domains. The flexibility of our method allows either inner or outer approximations of Lipschitz domains which also possess weakly defined curvatures, namely, domains whose boundary can be locally described as the graph of a function belonging to the Sobolev space $$W^{2,q}$$
W
2
,
q
for some $$q\ge 1$$
q
≥
1
. The sequences of approximating sets is also characterized by uniform isocapacitary estimates with respect to the initial domain $$\Omega $$
Ω
.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Università degli Studi di Firenze
Publisher
Springer Science and Business Media LLC
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