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arXiv · 1902.04777

On some properties of relative capacity and thinness in weighted variable exponent Sobolev spaces

Cihan Unal·Ismail Aydin
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Abstract

In this paper, we define weighted relative $p(.)$-capacity and discuss properties of capacity in the space $W_{\vartheta }^{1,p(.)}(\mathbb{R}^{n}).$ Also, we investigate some properties of weighted variable Sobolev capacity. It is shown that there is a relation between these two capacities. Moreover, we introduce a thinness in sense to this new defined relative capacity and prove an equivalence statement for this thinness.

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Cihan Unal, Ismail Aydin. 2019-02-13. On some properties of relative capacity and thinness in weighted variable exponent Sobolev spaces. https://doi.org/10.1007/s10476-020-0014-1

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