Evolution variational inequalities with general costs

Pierre Cyril Aubin-Frankowski; Giacomo Enrico Sodini; Ulisse Stefanelli

doi:10.1016/j.jfa.2026.111469

Evolution variational inequalities with general costs

Pierre Cyril Aubin-Frankowski
, Giacomo Enrico Sodini
, Ulisse Stefanelli

C/o Faculty of Mathematics of the University of Vienna
University of Vienna

Research output: Contribution to journal › Article › peer-review

Abstract

We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions c, including Bregman and entropic transport divergences. We establish several properties of the resulting flows for semiconvex functionals, including stability and energy identities. Using novel notions of convexity related to costs c, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.

Original language	English
Article number	111469
Journal	Journal of Functional Analysis
Volume	291
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2026.111469
Publication status	Published - 1 Jul 2026

Keywords

Cross-convexity
Evolution Variational Inequality
Gradient flows
Minimizing movements

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10.1016/j.jfa.2026.111469

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title = "Evolution variational inequalities with general costs",

abstract = "We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions c, including Bregman and entropic transport divergences. We establish several properties of the resulting flows for semiconvex functionals, including stability and energy identities. Using novel notions of convexity related to costs c, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.",

keywords = "Cross-convexity, Evolution Variational Inequality, Gradient flows, Minimizing movements",

author = "Aubin-Frankowski, \{Pierre Cyril\} and Sodini, \{Giacomo Enrico\} and Ulisse Stefanelli",

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AU - Aubin-Frankowski, Pierre Cyril

AU - Sodini, Giacomo Enrico

AU - Stefanelli, Ulisse

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N2 - We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions c, including Bregman and entropic transport divergences. We establish several properties of the resulting flows for semiconvex functionals, including stability and energy identities. Using novel notions of convexity related to costs c, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.

AB - We extend the theory of gradient flows beyond metric spaces by studying evolution variational inequalities (EVIs) driven by general cost functions c, including Bregman and entropic transport divergences. We establish several properties of the resulting flows for semiconvex functionals, including stability and energy identities. Using novel notions of convexity related to costs c, we prove that EVI flows are the limit of splitting schemes, providing assumptions for both implicit and explicit iterations.

KW - Cross-convexity

KW - Evolution Variational Inequality

KW - Gradient flows

KW - Minimizing movements

UR - https://www.scopus.com/pages/publications/105034695143

U2 - 10.1016/j.jfa.2026.111469

DO - 10.1016/j.jfa.2026.111469

M3 - Article

AN - SCOPUS:105034695143

SN - 0022-1236

VL - 291

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

M1 - 111469

ER -

Evolution variational inequalities with general costs

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Keywords

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