A characterization of convex calibrable sets in \(\mathbb R^N\)

DOI10.1007/s00208-004-0628-9zbMath1108.35073OpenAlexW2101745321MaRDI QIDQ1779183

Vincent Caselles, François Alter, Antonin Chambolle

Publication date: 1 June 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-004-0628-9

zbMATH Keywords

mean curvaturecalibrable sets

Mathematics Subject Classification ID

Variational inequalities (49J40) Degenerate parabolic equations (35K65) Degenerate elliptic equations (35J70)

Related Items (53)

Some remarks on the staircasing phenomenon in total variation-based image denoising ⋮ Gradient flows in metric random walk spaces ⋮ Singular solutions, graded meshes,and adaptivity for total-variation regularized minimization problems ⋮ An augmented Lagrangian model for signal segmentation ⋮ 1-Laplacian type problems with strongly singular nonlinearities and gradient terms ⋮ On total variation minimization and surface evolution using parametric maximum flows ⋮ Double-porosity homogenization for perimeter functionals ⋮ Isoperimetric inequalities in unbounded convex bodies ⋮ Anisotropic mean curvature on facets and relations with capillarity ⋮ An Overview on the Cheeger Problem ⋮ On a degenerate problem in the calculus of variations ⋮ On the Cheeger problem for rotationally invariant domains ⋮ Existence of self-Cheeger sets on Riemannian manifolds ⋮ Representation, relaxation and convexity for variational problems in Wiener spaces ⋮ Motion by crystalline-like mean curvature: A survey ⋮ The Cheeger cut and Cheeger problem in metric graphs ⋮ Adaptive anisotropic total variation: analysis and experimental findings of nonlinear spectral properties ⋮ Multiscale hierarchical decomposition methods for ill-posed problems ⋮ Asymptotic profiles of nonlinear homogeneous evolution equations of gradient flow type ⋮ The Cheeger cut and Cheeger problem in metric measure spaces ⋮ Isoperimetric sets and \(p\)-Cheeger sets are in bijection ⋮ Unbounded periodic constant mean curvature graphs on calibrable Cheeger Serrin domains ⋮ The Cheeger problem in abstract measure spaces ⋮ Geometric properties of solutions to the total variation denoising problem ⋮ On the jump set of solutions of the total variation flow ⋮ Periodic total variation flow of non-divergence type in \(\mathbb R^n\) ⋮ A characterization of convex calibrable sets in \(\mathbb R^N\) with respect to anisotropic norms ⋮ Large solutions for nonlinear parabolic equations without absorption terms ⋮ Inverse scale space decomposition ⋮ Morrey spaces and generalized Cheeger sets ⋮ Cheeger sets for rotationally symmetric planar convex bodies ⋮ Occupational measures and averaged shape optimization ⋮ On some nonlinear partial differential equations involving the 1-Laplacian ⋮ Regularity for solutions of the total variation denoising problem ⋮ The Dirichlet problem for singular elliptic equations with general nonlinearities ⋮ On boundary detachment phenomena for the total variation flow with dynamic boundary conditions ⋮ Uniqueness of the Cheeger set of a convex body ⋮ Structural analysis of an \(L\)-infinity variational problem and relations to distance functions ⋮ Total Variation in Imaging ⋮ Total variation and Cheeger sets in Gauss space ⋮ Some remarks on uniqueness and regularity of Cheeger sets ⋮ Linkage Between Piecewise Constant Mumford--Shah Model and Rudin--Osher--Fatemi Model and Its Virtue in Image Segmentation ⋮ The total variation flow in metric random walk spaces ⋮ Non-unique solutions for a convex TV – L¹ problem in image segmentation ⋮ A note on Cheeger sets ⋮ A PROJECTION APPROACH TO THE NUMERICAL ANALYSIS OF LIMIT LOAD PROBLEMS ⋮ Solution paths of variational regularization methods for inverse problems ⋮ Nonlocal perimeter, curvature and minimal surfaces for measurable sets ⋮ On the taut string interpretation and other properties of the Rudin-Osher-Fatemi model in one dimension ⋮ Minimizers of the prescribed curvature functional in a Jordan domain with no necks ⋮ The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising ⋮ Large solutions for the elliptic 1-Laplacian with absorption ⋮ The isoperimetric problem in 2d domains without necks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A parabolic quasilinear problem for linear growth functionals
• The total variation flow in \(\mathbb R^N\)
• Pairings between measures and bounded functions and compensated compactness
• Existence and non existence of capillary surfaces
• On the existence of capillary free surfaces in the absence of gravity
• Frontiere orientate di curvatura media assegnata in \(L^p\)
• Existence and regularity of a capillary surface with prescribed contact angle
• On capillary free surfaces in the absence of gravity
• On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions
• Area minimizing sets subject to a volume constraint in a convex set
• The curvature of a set with finite area
• An algorithm for total variation minimization and applications
• Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow
• Minimizing total variation flow
• An algorithm for mean curvature motion
• Un principio di massimo forte per le frontiere minimali e una sua applicazione alla risoluzione del problema al contorno per l'equazione delle superfici di area minima
• A subsidiary variational problem and existence criteria for capillary surfaces.
• Weakly Differentiable Functions
• Bounds for vertical points of solutions of prescribed mean curvature type equations, I
• Explicit Solutions of the Eigenvalue Problem $div \left(\frac Du\vert Du \vert \right)=u$ in $R^2$
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Isoperimetric regions in rotationally symmetric convex bodies
• The Dirichlet problem for the total variation flow
• On a crystalline variational problem. II: \(BV\) regularity and structure of minimizers on facets
• Characterization of facet breaking for nonsmooth mean curvature flow in the convex case

This page was built for publication: A characterization of convex calibrable sets in \(\mathbb R^N\)