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Risultati recenti e problemi aperti nel trattamento Semi-Lagrangiano di leggi di bilancio nonlineari

Gli schemi Semi-Lagrangiani (SL) sono abitualmente applicati in campi quali fluidodinamica ambientale, fisica dei plasmi ed equazioni di Hamilton-Jacobi, ma la loro applicazione a leggi di bilancio no...

A non-compactness result on the fractional Yamabe problem in large dimensions

Let (Xn+1,g+) be an (n+1)-dimensional asymptotically hyperbolic manifold with a conformal infinity (Mn,h). The fractional Yamabe problem addresses to solve Pγ[g+,h](u)=cun+2γn−2γ, u>0 on M whe...

On the De Giorgi conjecture for nonlocal equations with general kernels

I will describe recent results dealing with a nonlocal version of the De Giorgi conjecture on flatness of level sets for solutions of semi linear equ The first results obtained in this direction were ...

Use and misuse of mathematics in economic theory

Abstract: In recent decades the role of mathematics in then analysis of economic and financial phenomena has greatly increased.Unfortunately, the effects of such a process have not always been positiv...

Exact solution for rain-water flows and numerical simulation of surface runoff

We are interested in modeling and simulating surface runoff in urban areas during extreme rainfall events. We propose an extended Saint-Venant system which incorporates an additional rain term on the ...

Equazioni paraboliche quasilineari con energia non convessa

Soluzioni a valori misure di Young e di Radon intervengono in modo naturale nello studio di equazioni paraboliche quasilineari con energia non convessa (o equazioni forward-backward). Saranno presenta...

Variational methods for photometric 3D-reconstruction

Energy minimization methods have been shown to be particularly effective for solving a wide class of inverse problems in computer vision and image processing. Variational methods are energy minimizati...

Morse-Sard type theorems for Sobolev mappings

The Morse-Sard theorem, and the generalizations by Dubovitskiui and Federer, have numerous applications and belong to the core results of multivariate calculus for smooth mappings. In this talk we dis...