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arXiv · 2004.08448

Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents

Wojciech Górny
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Abstract

In the setting of metric measure spaces satisfying the doubling condition and the $(1,p)$-Poincar\'e inequality, we prove a metric analogue of the Bourgain-Brezis-Mironescu formula for functions in the Sobolev space $W^{1,p}(X,d,\nu)$, under the assumption that for $\nu$-a.e. point the tangent space in the Gromov-Hausdorff sense is Euclidean with fixed dimension $N$.

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BibTeXRIS

Wojciech Górny. 2020-04-17. Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents. https://arxiv.org/abs/2004.08448

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