Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations

DOI10.1137/23m1569873arXiv2304.04729OpenAlexW4392374135MaRDI QIDQ6195326

Nicola Picenni, Massimo Gobbino

Publication date: 13 March 2024

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.04729

zbMATH Keywords

total variationmaximum principlegeneralized solutionssemidiscrete schemePerona-Malik equationforward-backward parabolic equation

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Discrete version of topics in analysis (39A12) Weak solutions to PDEs (35D30) Quasilinear parabolic equations (35K59)

Cites Work

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• Gradient estimates for the Perona-Malik equation
• Convergence of discrete schemes for the Perona-Malik equation
• A new nonlocal nonlinear diffusion of image processing
• Conjectures on some evolution problems
• On a class of forward-backward parabolic equations: formation of singularities
• Existence of infinitely many solutions for the one-dimensional Perona-Malik model
• CONVERGENCE FOR LONG-TIMES OF A SEMIDISCRETE PERONA–MALIK EQUATION IN ONE DIMENSION
• Slow Time Behavior of the Semidiscrete Perona–Malik Scheme in One Dimension
• The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type
• The zero set of a solution of a parabolic equation.
• Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
• The Perona--Malik Paradox
• On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems
• Measure-Valued Solutions to a Nonlinear Fourth-Order Regularization of Forward-Backward Parabolic Equations
• An analysis of the Perona-Malik scheme
• Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions
• Global Solutions to the Gradient Flow Equation of a Nonconvex Functional
• A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional

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