Abstract
AbstractWe reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involved in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be $$W^{1,\,q}$$
W
1
,
q
-extension domain when $$2<q<\infty$$
2
<
q
<
∞
.
Funder
European Research Council
ETH Zurich
Publisher
Springer Science and Business Media LLC
Subject
General Earth and Planetary Sciences,General Environmental Science
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