Gradient flows of $$(K,\!N)$$-convex functions with negative N
Abstract
Abstract We discuss $$(K,\!N)$$ ( K , N ) -convexity and gradient flows for $$(K,\!N)$$ ( K , N ) -convex functionals on metric spaces, in the case of real K and negative N . In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaining as values both the positive and the negative infinity. We prove several properties of gradient flows of $$(K,\!N)$$ ( K , N ) -convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Optimization and Variational Analysis
Analytic and geometric function theory
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 65
- Issue
- 3
- Publication date
- 17 February 2026
- Language
- EN