[BOOK][B] Variational methods in imaging

O Scherzer, M Grasmair, H Grossauer, M Haltmeier… - 2009 - Springer
Imaging is an interdisciplinary research area with profound applications in many areas of
science, engineering, technology, and medicine. The most primitive form of imaging is visual …

[BOOK][B] Calculus of variations

F Rindler - 2018 - Springer
The calculus of variations has its roots in the first problems of optimality studied in classical
antiquity by Archimedes (ca. 287–212 BC in Syracuse, Magna Graecia) and Zenodorus (ca …

Existence and convergence for quasi‐static evolution in brittle fracture

GA Francfort, CJ Larsen - … on Pure and Applied Mathematics: A …, 2003 - Wiley Online Library
This paper investigates the mathematical well‐posedness of the variational model of quasi‐
static growth for a brittle crack proposed by Francfort and Marigo in [15]. The starting point is …

A global method for relaxation

G Bouchitté, I Fonseca, L Mascarenhas - Archive for rational mechanics …, 1998 - Springer
A new method for the identification of the integral representation of a class of functionals
defined on BV(Ω;\BbbR^d)*\calA(Ω) (where \calA(Ω) represents the family of open subsets of …

[PDF][PDF] Relaxation of signed integral functionals in BV

J Kristensen, F Rindler - Calculus of Variations and Partial Differential …, 2010 - Citeseer
d| Dsu|, u∈ BV (Ω; Rm), when the integrand f: Rm× d→ R is continuous, of linear growth at
infinity and possibly unbounded below. All previous results in the BV context concerned …

Stochastic homogenization of degenerate integral functionals with linear growth

M Ruf, CI Zeppieri - Calculus of Variations and Partial Differential …, 2023 - Springer
We study the limit behaviour of sequences of non-convex, vectorial, random integral
functionals, defined on W 1, 1, whose integrands are ergodic and satisfy degenerate linear …

Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy

S Conti, M Focardi, F Iurlano - Archive for Rational Mechanics and …, 2024 - Springer
We consider a family of vectorial models for cohesive fracture, which may incorporate SO (n)-
invariance. The deformation belongs to the space of generalized functions of bounded …

A global method for deterministic and stochastic homogenisation in BV

F Cagnetti, G Dal Maso, L Scardia, CI Zeppieri - Annals of PDE, 2022 - Springer
In this paper we study the deterministic and stochastic homogenisation of free-discontinuity
functionals under linear growth and coercivity conditions. The main novelty of our …

Lower semicontinuity and Young measures in BV without Alberti's Rank-One Theorem

F Rindler - 2012 - degruyter.com
We give a new proof of sequential weak* lower semicontinuity in for integral functionals of
the form where and is a quasiconvex Carathéodory integrand with linear growth at infinity, ie …

A relaxation result in the framework of structured deformations in a bounded variation setting

M Baía, J Matias, PM Santos - Proceedings of the Royal Society of …, 2012 - cambridge.org
We obtain an integral representation of an energy for structured deformations of continua in
the space of functions of bounded variation, as a first step to the study of asymptotic models …