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An introduction to Total Variation for Image Analysis
These are the lecture notes of a course taught in Linz in Sept., 2009, at the school "summer school on sparsity", organized by Massimo Fornasier and Ronny Romlau. They address various theoretical and
The Total Variation Flow in RN
The purpose of this chapter is to prove existence and uniqueness of the minimizing total variation flow in ℝ N $$ \frac{{\partial u}} {{\partial t}} = div\left( {\frac{{Du}} {{\left| {Du}
The p-Laplace eigenvalue problem as p goes to 1 and Cheeger sets in a Finsler metric
We consider the p–Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for p > 1, we investigate the limit
On a Crystalline Variational Problem, Part I:¶First Variation and Global L∞ Regularity
Abstract:Let φ:ℝn→ [0,+∞[ be a given positively one-homogeneous convex function, and let ?φ≔{φ≤ 1 }. Pursuing our interest in motion by crystalline mean curvature in three dimensions, we introduce
Facet-breaking for three-dimensional crystals evolving by mean curvature
We show two examples of facet-breaking for three-dimensional polyhedral surfaces evolving by crystalline mean curvature. The analysis shows that creation of new facets during the evolution is a
The Discontinuity Set of Solutions of the TV Denoising Problem and Some Extensions
The main purpose of this paper is to prove that the jump discontinuity set of the solution of the total variation based denoising problem is contained in the jump set of the datum to be denoised. We
Motion by Curvature of Planar Networks
We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical
Existence of Traveling Waves of Invasion for Ginzburg–Landau-type Problems in Infinite Cylinders
We study a class of systems of reaction–diffusion equations in infinite cylinders which arise within the context of Ginzburg–Landau theories and describe the kinetics of phase transformation in
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