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We prove that a reaction-diiusion inclusion provides a sub-optimal approximation for anisotropic motion by mean curvature in the non-smooth case. This result is valid in any space dimension and withâ€¦ (More)

- Antonin Chambolle, V. Caselles, Matteo Novaga, D. Cremersand, Thomas Pock
- 2009

These notes address various theoretical and practical topics related to Total Variation-based image reconstruction. They focuse first on some theoretical results on functions which minimize the totalâ€¦ (More)

In their classical 1937 paper, Kolmogorov, Petrovsky and Piskunov proved that for a particular class of reaction-diffusion equations on the real line the solution of the initial value problem withâ€¦ (More)

We study a class of systems of reactionâ€“diffusion equations in infinite cylinders which arise within the context of Ginzburgâ€“Landau theories and describe the kinetics of phase transformation inâ€¦ (More)

- Giovanni Bellettini, Al-hassem Nayam, Matteo Novaga
- Asymptotic Analysis
- 2015

In this paper we prove an asymptotic estimate, up to the second order included, on the behaviour of the one-dimensional Allen-Cahnâ€™s action functionals, around a periodic function with boundedâ€¦ (More)

We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For aâ€¦ (More)

- Vicent Caselles, Antonin Chambolle, Matteo Novaga
- Multiscale Modeling & Simulation
- 2007

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. Weâ€¦ (More)

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flowâ€¦ (More)

- Antonin Chambolle, Matteo Novaga
- SIAM J. Math. Analysis
- 2006

We give a simple proof of convergence of the anisotropic variant of a well-known algorithm for mean curvature motion, introduced in 1992 by Merriman, Bence, and Osher. The algorithm consists inâ€¦ (More)

We prove that if C âŠ‚ R is of class C and uniformly convex, then the Cheeger set of C is unique. The Cheeger set of C is the set which minimizes, inside C, the ratio perimeter over volume.