arXiv subjects

Michael Goldman

Publications and source records attributed to Michael Goldman.

60 records · Page 4Linked to original sources

arXiv2013

The $Γ$-limit for singularly perturbed functionals of Perona-Malik type in arbitrary dimension

In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $Γ$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the space of special functions of bounded variation with vanishing diffuse gradient part. This provides a direction of investigation to derive approximation for functionals with discontinuities penalized with a "cohesive" energy, that is, whose cost depends on the actual opening of the discontinuity.

math.AP↗

arXiv2012

Plane-like minimizers and differentiability of the stable norm

In this paper we investigate the strict convexity and the differentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly elliptic case). We prove that it is always differentiable in totally irrational directions, while in other directions, it is differentiable if and only if the corresponding plane-like minimizers satisfying a strong Birkhoff property foliate the torus. We also discuss the issue of the uniqueness of the correctors for the corresponding homogenization problem.

math.AP↗

arXiv2012

Representation, relaxation and convexity for variational problems in Wiener spaces

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework.

math.AP↗

arXiv2011

A geometric approach for convexity in some variational problem in the Gauss space

In this short note we prove the convexity of minimizers of some variational problem in the Gauss space. This proof is based on a geometric version of an older argument due to Korevaar.

math.AP↗

arXiv2011

Approximation and relaxation of perimeter in the Wiener space

We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L^2-topology. We also show that the rescaled Allen-Cahn functionals approximate this relaxed functional in the sense of Gamma-convergence.

math.AP↗

arXiv2010

Continuous Primal-Dual Methods for Image Processing

In this article we study a continuous Primal-Dual method proposed by Appleton and Talbot and generalize it to other problems in image processing. We interpret it as an Arrow-Hurwicz method which leads to a better description of the system of PDEs obtained. We show existence and uniqueness of solutions and get a convergence result for the denoising problem. Our analysis also yields new a posteriori estimates.

math.AP↗