Calculus of Variations & PDEs
My research in the calculus of variations focuses on functional analysis and its applications to mechanics and image processing. A key area of interest is the study of Γ-convergence, relaxation, homogenization, and free-discontinuity problems.
In collaboration with S. Amstutz and A. Novotny, I have worked on interfaces and free boundaries (IFB) and image processing (IPI), with applications to segmentation and classification. These works provide rigorous mathematical frameworks for understanding how variational principles can be applied to real-world problems.
Additionally, my work includes the study of bounded deformation and incompatibility operators, which are fundamental to understanding defects in solids.
Key Publications
Rigidity and Functional Properties of BDdev(Ω)
M. Caroccia, N. Van Goethem
Archive for Rational Mechanics and Analysis, 2026
Iterative blow-ups for maps with bounded 𝒜-variation: A refinement, with application to BD and BV
M. Caroccia, N. Van Goethem
Advances in Calculus of Variations, 2025
On integral representation of local energy functionals on BD
M. Caroccia, M. Focardi, N. Van Goethem
SIAM Journal on Mathematical Analysis, 2020
Minimal partitions and image classification with a gradient-free perimeter approximation
S. Amstutz, A. Novotny, N. Van Goethem
Inverse Problems and Imaging, 2014
Topology optimization methods with gradient-free perimeter approximation
S. Amstutz, N. Van Goethem
Interfaces and Free Boundaries, 2012
Topological sensitivity analysis for elliptic differential operators of order 2m
S. Amstutz, A. Novotny, N. Van Goethem
Journal of Differential Equations, 2014
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