Youcef Mammeri, Université de Picardie Jules Verne - Amiens, Asymptotic behavior of small solutions of the Benjamin-Ono equations, Friday, November 18, 2011, time 15:00 o'clock, Aula Seminari VI piano
Abstract:Abstract:
We study the behavior of small solutions depending on time of the generalized and regularized Benjamin-Ono equation in both continuous and periodic contexts. In particular, we prove that these solutions remain small. Moreover, we show that solutions are decreasing in the continuous case.

Alain Miranville, Universite de Poitiers, Asymptotic behavior of Caginalp phase-field systems, Friday, October 21, 2011, time 14:00 o'clock, Aula seminari III piano

Cristina Trombetti, Universita di Napoli Federico II, SU UN PROBLEMA DI BISEZIONE NEL PIANO E DISUGUAGLIANZE DI SOBOLEV- POINCARE, Thursday, May 26, 2011, time 12:15 o'clock, Aula seminari III piano
Abstract:Abstract:
We prove a long standing conjecture concerning the fencing problem in the plane: among planar convex sets of given area, prove that the disc, and only the disc maximizes the length of the shortest area-bisecting curve. Although it may look intuitive, the result is by no means trivial since we also prove that among planar convex sets of given area the set which maximizes the length of the shortest bisecting chords is the so-called Auerbach triangle.

Patrick Guidotti, University of California, Irvine, A New Forward-Backward Regularization of the Perona-Malik equation, Tuesday, March 22, 2011, time 15:00 o'clock, Aula Seminari VI piano
Abstract:Abstract:
The Perona-Malik equation (PME) is a forward-backward nonlinear diffusion which was proposed in the context of image processing as an image enhancement tool capable of preserving sharp features such as edges. To this day its mathematical nature has not been fully understood in spite of many an attempt. After a brief historical overview of the mathematical results available for the equation and its many regularizations/relaxations, the talk will introduce and analyze a novel, rather natural, regularization which will shed light on the nature of PME. The regularization is quite mild in that PME is regularized by a family of forward-backward equations, the solutions of which are, however, better behaved.

ENRICO VITALI, Universita` di Pavia, Un modello variazionale discreto del secondo ordine, Wednesday, March 16, 2011, time 11:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
We analyze a nonlinear discrete scheme depending on second-order finite differences. This is the two-dimensional analog of a scheme which in one dimension approximates a free-discontinuity energy proposed by Blake and Zisserman as a higher-order correction of the Mumford and Shah functional. In two dimension we give a compactness result showing that the continuous problem approximating this difference scheme is still defined on special functions with bounded hessian, and we give an upper and a lower bound in terms of the Blake and Zisserman energy.

GIACOMO CARBONI, Universita` del Salento, Image segmentation e inpainting: approccio variazionale e modellizzazione numerica, Wednesday, March 16, 2011, time 12:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
Si presentano risultati noti sull esistenza di minimi per il funzionale di Blake & Zisserman e l applicazione dello stesso al problema della segmentazione di immagini. Si introduce un metodo di approssimazione numerica per le equazioni di Eulero-Lagrange associate e si presentano i risultati dell analisi. Successivamente si presentano i risultati di esistenza per i minimi di un nuovo funzionale del secondo ordine e la sua applicazione al problema dell inpainting. La ricerca di una soluzione per le equazioni di Eulero-Lagrange associate viene affrontata in maniera analoga a quanto fatto nel caso della segmentazione. A completare la presentazione, alcuni accenni all analisi del metodo ed esempi.