Continuous limits of discrete perimeters
Antonin Chambolle (CMAP), Alessandro Giacomini, Luca Lussardi (DIMAT)
TL;DR
This paper investigates how certain discrete convex functionals, which satisfy a generalized coarea formula, behave as they transition to the continuum limit, providing insights into their asymptotic properties.
Contribution
It introduces a framework for analyzing the continuum limits of discrete convex functionals satisfying a generalized coarea formula, bridging discrete and continuous analysis.
Findings
Established convergence of discrete convex functionals to continuum limits
Provided conditions under which the coarea formula extends to the continuum
Enhanced understanding of the asymptotic behavior of discrete convex functionals
Abstract
We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.
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