Liero, Matthias and Mielke, Alexander and Savaré, Giuseppe
(2023)
*Fine properties of geodesics and geodesic lambda-convexity for the Hellinger-Kantorovich distance.*
Archive for Rational Mechanics and Analysis, 247
(112).

Full text not available from this repository.

Official URL: https://doi.org/10.1007/s00205-023-01941-1

## Abstract

We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger–Kantorovich problem (HK), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new regularity properties for the solution of the Hamilton–Jacobi equation arising in the dual dynamic formulation of HK, which are sufficiently strong to construct a characteristic transport-growth flow driving the geodesic interpolation between two arbitrary positive measures. These results are applied to study relevant geometric properties of HK geodesics and to derive the convex behaviour of their Lebesgue density along the transport flow. Finally, exact conditions for functionals defined on the space of measures are derived that guarantee the geodesic -convexity with respect to the Hellinger–Kantorovich distance. Examples of geodesically convex functionals are provided.

Item Type: | Article |
---|---|

Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3172 |

Deposited By: | Lukas-Maximilian Jaeger |

Deposited On: | 04 Sep 2024 12:17 |

Last Modified: | 04 Sep 2024 12:17 |

Repository Staff Only: item control page