Evolutionary variational inequalities on the Hellinger-Kantorovich and spherical Hellinger-Kantorovich spaces
Abstract
We study the minimizing movement scheme for families of geodesically semiconvex functionals defined on either the Hellinger-Kantorovich space or on the Spherical Hellinger-Kantorovich space. By exploiting some of the finer geometric properties of the spaces (namely the local-angle condition and the semiconcavity of the squared distance, when restricted to suitable subsets), we prove that the sequence of curves, which are produced by geodesically interpolating the points generated by the minimizing movement scheme, converges to a curve that satisfy the Evolutionary Variational Inequality (EVI), when the time step goes to 0. Under suitable conditions, we obtain a global EVI flow on the whole space.
Fields of Study & Subjects
Contact Mechanics and Variational Inequalities
Advanced Numerical Analysis Techniques
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Communications in Partial Differential Equations
- Publisher
- Informa UK Limited
- Volume
- 51
- Issue
- 2-3
- Pages
- 193–235
- Publication date
- 4 March 2026
- Language
- EN