On Sobolev extension domains in $R^n$

By Pavel Shvartsman. 2009

60 citations recorded by the source corpus.

We describe a class of Sobolev $W^k_p$-extension domains $\Omega\subset R^n$ determined by a certain inner subhyperbolic metric in $\Omega$. This enables us to characterize finitely connected Sobolev $W^1_p$-extension domains in $R^2$ for each $p>2$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c52cbe91a2a5a11f9e96b6d4bd25789bf649d68e

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In Applied Mathematics

1. Yuan Zhou
2. Dachun Yang
3. Luong Dang Ky
4. Wen Yuan
5. L. Ihnatsyeva
6. T. Heikkinen
7. Heli Tuominen

In Geometry and Topology

1. Yuan Zhou

Citations in the corpus

• Fractional Sobolev extension and imbedding (2014, background): “When p ∈ (2, ∞), Buckley, Koskela and Shvartsman proved that Ω is a W 1, -extension/-imbedding domain if and only if it is a weak (p − 2)/(p − 1)-cigar domain; see [3, 19, 25].”