| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 49 | |
| Number of page(s) | 25 | |
| DOI | https://doi.org/10.1051/cocv/2025036 | |
| Published online | 04 June 2025 | |
Weak geodesics on prox-regular subsets of Riemannian manifolds
1
IMI, Departamento de Análisis Matemático y Matemática Aplicada, Facultad Ciencias Matemáticas, Universidad Complutense,
28040
Madrid, Spain
2
Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan,
Isfahan
81746-73441, Iran
* Corresponding author: pourya@math.ui.ac.ir
Received:
19
March
2024
Accepted:
1
April
2025
We give a definition of weak geodesics on prox-regular subsets of Riemannian manifolds as continuous curves with some weak regularities. Then obtaining a suitable Lipschitz constant of the projection map, we characterize weak geodesics on a prox-regular set with assigned end points as viscosity critical points of the energy functional.
Mathematics Subject Classification: 58C20 / 58E10 / 49J52
Key words: Prox-regular sets / φ-convex sets / Sobolev spaces / metric projection / nonsmooth analysis / Riemannian manifolds
© The authors. Published by EDP Sciences, SMAI 2025
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