Free-discontinuity problems generated by singular perturbation
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Publication:4229269
DOI10.1017/S0308210500027256zbMath0920.49007MaRDI QIDQ4229269
Maria Stella Gelli, Andrea Braides, Roberto Alicandro
Publication date: 11 April 1999
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20)
Related Items (8)
REGULAR APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS ⋮ ON THE VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS IN THE VECTORIAL CASE ⋮ A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional ⋮ The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type ⋮ The Γ-limit for singularly perturbed functionals of Perona–Malik type in arbitrary dimension ⋮ An approximation of the Mumford--Shah energy by a family of discrete edge-preserving functionals ⋮ Unnamed Item ⋮ Non-local approximation of free-discontinuity problems with linear growth
Cites Work
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- A gradient approach to localization of deformation. I. Hyperelastic materials
- On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
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- Optimal approximations by piecewise smooth functions and associated variational problems
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- On Lower Semicontinuity of Integral Functionals. I
- On the non-local approximation of free-discontinuity problems
- Investigation of Modes of Constitutive Instability Manifestation in a One‐Dimensional Model
- Finite difference approximation of the Mumford-Shah functional
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