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arXiv · 2207.12191

Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces

Fabrice Baudoin
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Abstract

We present developments in the theory of Korevaar-Schoen-Sobolev spaces on metric measure spaces. While this theory coincides with those of Cheeger and Shanmugalingam if the space is doubling and satisfies a Poincar\'e inequality, it offers new perspectives in the context of fractals for which the approach by weak upper gradients is inadequate.

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Fabrice Baudoin. 2022-07-25. Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces. https://arxiv.org/abs/2207.12191

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