Zobrazeno 1 - 10
of 148
pro vyhledávání: '"Savare, Giuseppe"'
We propose a generalization, where negative weights are allowed, of the Wasserstein barycenter of $n$ probability measures. The barycenter is found, as usual, as a minimum of a functional. In this paper, we prove existence of a minimizer for probabil
Externí odkaz:
http://arxiv.org/abs/2411.06838
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex envelope of a co
Externí odkaz:
http://arxiv.org/abs/2401.00542
We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport. The discrete
Externí odkaz:
http://arxiv.org/abs/2312.13284
Autor:
Rossi, Riccarda, Savaré, Giuseppe
We introduce the concept of action space, a set $\boldsymbol{X}$ endowed with an action cost $\mathsf{a}:(0,+\infty)\times \boldsymbol{X}\times \boldsymbol{X}\to [0,+\infty)$ satisfying suitable axioms, which turn out to provide a `dynamic' generaliz
Externí odkaz:
http://arxiv.org/abs/2311.01841
We introduce and study the class of totally dissipative multivalued probability vector fields (MPVF) $\boldsymbol{\mathrm F}$ on the Wasserstein space $(\mathcal{P}_2(\mathsf{X}),W_2)$ of Euclidean or Hilbertian probability measures. We show that suc
Externí odkaz:
http://arxiv.org/abs/2305.05211
Publikováno v:
Canadian Journal of Mathematics. Published online 2023:1-38
We study monotone operators in reflexive Banach spaces that are invariant with respect to a group of suitable isometric isomorphisms and we show that they always admit a maximal extension which preserves the same invariance. A similar result applies
Externí odkaz:
http://arxiv.org/abs/2305.04678
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz functions in the metric-Sobolev space $H^{1,p}(X,\mathsf{d},\mathfrak{m})$ associated with a positive and finite Borel measure $\mathfrak{m}$ in a separable a
Externí odkaz:
http://arxiv.org/abs/2209.00974
Fine properties of geodesics and geodesic $\lambda$-convexity for the Hellinger-Kantorovich distance
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 p
Externí odkaz:
http://arxiv.org/abs/2208.14299
Autor:
Mazzoleni, Dario, Savaré, Giuseppe
We study the $L^2$-gradient flow of functionals $\mathcal F$ depending on the eigenvalues of Schr\"odinger potentials $V$ for a wide class of differential operators associated to closed, symmetric, and coercive bilinear forms, including the case of a
Externí odkaz:
http://arxiv.org/abs/2203.07304
Publikováno v:
In Journal de mathématiques pures et appliquées August 2024 188:114-178
