The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type
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Publication:3522293
DOI10.1090/S0002-9947-08-04495-4zbMath1191.49010OpenAlexW2033377980MaRDI QIDQ3522293
Giorgio Fusco, Giovanni Bellettini
Publication date: 1 September 2008
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9947-08-04495-4
Sensitivity, stability, well-posedness (49K40) Variational methods involving nonlinear operators (47J30) Singular perturbations in context of PDEs (35B25) Methods involving semicontinuity and convergence; relaxation (49J45) Variational methods for second-order elliptic equations (35J20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
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Classification of equilibria and \(\Gamma \)-convergence for the discrete Perona-Malik functional ⋮ PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW ⋮ A qualitative description of microstructure formation and coarsening phenomena for an evolution equation ⋮ A model for staircase formation in fingering convection ⋮ On Lipschitz solutions for some forward-backward parabolic equations ⋮ A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional ⋮ Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations ⋮ Upper bounds on the coarsening rate of discrete, ill‐posed nonlinear diffusion equations ⋮ A backward-forward regularization of the Perona-Malik equation ⋮ CONVERGENCE FOR LONG-TIMES OF A SEMIDISCRETE PERONA–MALIK EQUATION IN ONE DIMENSION ⋮ Solitary waves for an equation related to a problem of microstructure formation ⋮ The Γ-limit for singularly perturbed functionals of Perona–Malik type in arbitrary dimension ⋮ Radial weak solutions for the Perona-Malik equation as a differential inclusion ⋮ A new nonlocal nonlinear diffusion of image processing ⋮ An Example of Global Classical Solution for the Perona-Malik Equation ⋮ A class of local classical solutions for the one-dimensional Perona-Malik equation ⋮ Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions
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