Personne

Maria Colombo

Publications associées (51)

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A global existence result for the semigeostrophic equations in three dimensional convex domains

Maria Colombo

Exploiting recent regularity estimates for the Monge-Ampère equation, under some suitable assumptions on the initial data we prove global-in-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domain ...

2014

A Global Existence Result for the Semigeostrophic Equations in Three Dimensional Convex Domains

Maria Colombo

Exploiting recent regularity estimates for the Monge-Ampere equation, under some suitable assumptions on the initial data we prove global in-time existence of Eulerian distributional solutions to the semigeostrophic equations in 3-dimensional convex domain ...

2014

Obstructions to regularity in the classical Monge problem

Maria Colombo

We provide counterexamples to regularity of optimal maps in the classical Monge problem under various assumptions on the initial data. Our construction is based on a variant of the counterexample in [10] to Lipschitz regularity of the monotone optimal map ...

2014

Regularity results for very degenerate elliptic equations

Maria Colombo

We consider a family of elliptic equations introduced in the context of traffic congestion. They have the form del . (del F(del u)) = f where F is a convex function which vanishes inside some convex set and is elliptic outside. Under some natural assumptio ...

2014

Rigidity of equality cases in Steiner’s perimeter inequality

Maria Colombo

Characterization results for equality cases and for rigidity of equality cases in Steiner’s perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner symmetral under considerati ...

2014

An Excess-Decay Result for a Class of Degenerate Elliptic Equations

Maria Colombo

We consider a family of degenerate elliptic equations of the form div(del F(del u)) = f, where F is an element of C-1,C-1 is a convex function which is elliptic outside a ball. We prove an excess-decay estimate at points where del u is close to a nondegene ...

2014

In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampere equations, recently established by De Philippis and Figalli [14], to provide global in time existence of distributional solutions to the semigeostrophic ...

2012

The problem of multi-target tracking of deforming objects in video sequences arises in many situations in image processing and computer vision. Many algorithms based on finite dimensional particle filters have been proposed. Recently, particle filters for ...

Springer Berlin Heidelberg2012

We prove that solutions of a mildly regularized Perona–Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the gener ...

2012

We consider the long time behavior of the semidiscrete scheme for the Perona-Malik equation in one dimension. We prove that approximated solutions converge, in a slow time scale, to solutions of a limit problem. This limit problem evolves piecewise constan ...

2011