On the singularities of distance functions in Hilbert spaces

DOI10.1007/S00013-024-01987-XzbMATH Open1548.49022MaRDI QIDQ6536633

Thomas Strömberg

Publication date: 13 May 2024

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

Hilbert spacecomponentssingular setpropagation of singularitiesintrinsic characteristic

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Fréchet and Gateaux differentiability in optimization (49J50) Classification of homotopy type (55P15) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Cites Work

• Title not available (Why is that?)
• The nearest point mapping is single valued nearly everywhere
• A remark on regularization in Hilbert spaces
• Generalized characteristics and Lax-Oleinik operators: global theory
• Singular gradient flow of the distance function and homotopy equivalence
• Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
• Singularities of solutions of Hamilton-Jacobi equations
• Fréchet differentiability of convex functions
• Unbounded components of the singular set of the distance function in \(\mathbb{R}^n\)
• Metric projections and the differentiability of distance functions
• A Connectedness Property of Maximal Monotone Operators and its Application to Approximation Theory
• Cardinality of the metric projection on typical compact sets in Hilbert spaces
• Distance functions with dense singular sets
• Cebysev Sets in Hilbert Space
• Propagation of singularities of Moreau envelopes and distance functions in a Hilbert space

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