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

Fabrice Baudoin

doi:10.54330/AFM.147513

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

^*Corresponding author for this work

Department of Mathematics

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2 Citations (Scopus)

Abstract

We survey, unify and present new 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 supports a Poincaré inequality, it offers new perspectives in the context of fractals for which the approach by weak upper gradients is inadequate.

Original language	English
Journal	Annales Fennici Mathematici
Volume	49
Issue	2
Pages (from-to)	487-527
Number of pages	41
ISSN	2737-0690
DOIs	https://doi.org/10.54330/AFM.147513
Publication status	Published - 2024

Keywords

Fractals
Korevaar–Schoen space
Sobolev spaces

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10.54330/AFM.147513Licence: CC BY-NC

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Cite this

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

Abstract

Keywords

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