平面上容量的对偶性和Sobolev可扩展性。

Complex analysis and its synergies Pub Date : 2021-01-01 Epub Date: 2021-02-22 DOI:10.1007/s40627-021-00063-2

Yi Ru-Ya Zhang

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引用次数: 2

摘要

揭示了平面上容量的对偶性与Jordan域的Sobolev可扩展性之间的关系，并解释了如何通过容量的对偶性来解读Jordan域的Sobolev可扩展性所涉及的曲线条件。最后作为应用，给出了平面约当域在2q∞时为w1, q -可拓域的必要条件的替代证明。

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Duality of capacities and Sobolev extendability in the plane.

We 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 $W^{1, q}$ -extension domain when $2 < q < \infty$ .

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来源期刊

Complex analysis and its synergies

CiteScore

1.10

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0.00%

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