Work

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

Year: 2024

Type: article

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.

Source: Annales Fennici Mathematici

DOI: 10.54330/afm.147513

Author: Fabrice Baudoin

Institution: Aarhus University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Geometric and Functional Inequalities in Sub-Riemannian and Non-Smooth Dirichlet Spaces and Analysis of Random Rough Paths, Some topics in Analysis and Probability in Metric Measure Spaces, Random Matrices, and Diffusions