Linus Wiegmann | Approximation order of Kolmogorov, Gel'fand and linear diameters for Sobolev embeddings in Euclidean measure spaces

Startdatum: 06.07.2023 - 14:15
Enddatum: 06.07.2023 - 15:45
Adresse: MZH 4140
Preis: 0€

Based on the joint work with Marc Keßeböhmer, I will introduce our methods that solved the problem of finding the upper, resp. lower approximation order with respect to the Kolmogorov, Gel’fand and linear diameters for the embedding of the Sobolev spaces Wα, p and W0α, p in the Euclidean measure space Lνq for an arbitrary Borel probability measure ν with support contained in the open m-dimensional unit cube and for all possible choices of p, q between 1 and infinity. Further, underlying concepts, such as the Lq-spectrum of the measure ν will be introduced, which admits a connection between the approximation order and the fractal geometric notion of the Minkowski dimension of the support of ν. The exact values of the (upper) approximation orders are given in terms of this Lq-spectrum only and provide sufficient conditions imposed on the regularity of ν for approximation order to exist.