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arXiv · 2304.06561

Nguyen's approach to Sobolev spaces in metric measure spaces with unique tangents

Camillo Brena·Andrea Pinamonti
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Abstract

We extend Nguyen's characterization of Sobolev spaces $W^{1,p}$ to the setting of PI-metric measure spaces such that at a.e. point the tangent space (in the Gromov-Hausdorff sense) is unique and Euclidean with a fixed dimension. We also generalize [CLL14] to PI-metric measure spaces such that at a.e. point the tangent space is unique and equal to the Heisenberg group with a fixed homogeneous dimension. The approach is easier and completely different from the one in [Ngu06, Ngu08].

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Camillo Brena, Andrea Pinamonti. 2023-04-13. Nguyen's approach to Sobolev spaces in metric measure spaces with unique tangents. https://arxiv.org/abs/2304.06561

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