5 papers
Sharp Rates of MMD Empirical Estimation with Power Kernels
Francesco Colasanto, Matteo Focardi, Massimo Fornasier +1
We establish quantitative rates of convergence for the empirical estimation of probability measures by means of the Maximum Mean Discrepancy (MMD) with power kernel $K_q(x,y) = -|x…
Homogenisation of phase-field functionals with linear growth
Francesco Colasanto, Matteo Focardi, Caterina Ida Zeppieri
We propose a first rigorous homogenisation procedure in image-segmentation models by analysing the relative impact of (possibly random) fine-scale oscillations and phase-field regu…
Phase-field modelling of cohesive fracture. Part I: -convergence results
Roberto Alessi, Francesco Colasanto, Matteo Focardi
The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture. In this first paper we establish the mathematic…
Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application
Roberto Alessi, Francesco Colasanto, Matteo Focardi
This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical found…
Phase-field modelling of cohesive fracture. Part II: Reconstruction of the cohesive law
Roberto Alessi, Francesco Colasanto, Matteo Focardi
This is the second paper of a three-part work the main aim of which is to provide a unified consistent framework for the phase-field modelling of cohesive fracture. Building on the…