Geodesic
Korevaar–Schoen–Sobolev spaces and critical exponents in metric measure spaces
Fabrice Baudoin1
1Aarhus University, Department of Mathematics
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 487–527

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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.  
DOI : 10.54330/afm.147513
Keywords: Fractals, Sobolev spaces, Korevaar–Schoen space

Fabrice Baudoin  1

1 Aarhus University, Department of Mathematics 
Fabrice Baudoin. Korevaar–Schoen–Sobolev spaces and critical exponents in metric measure spaces. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 487–527. doi: 10.54330/afm.147513
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