Seminari di Equazioni alle Derivate Parziali e Calcolo delle Variazioni


Informazioni e contatti: Lorenzo Giacomelli, Luisa Moschini, Angela Pistoia

Seminari tenuti nel 2010





10.02 Sanjiban Santra (U. Sydney) - On a fourth order problem  with large exponents

We analyze the blow up phenomena of bounded integrable solutions of a semilinear fourth order elliptic problem with a large exponent under zero Dirichlet boundary conditions. We extend the results obtained by Ren-Wei, Adimurthi-Grossi, Esposito-Musso-Pistoia  to the biharmonic case.  The results obtained are new even for the second order case.

17.02 Norman Dancer (U. Sydney) -  Systems of nonlinear elliptic equations on $R^N$ or balls

We obtain branches of solutions of these equations by combining bifurcation theory and finite Morse index ideas (joint work with T. Bartsch and Z.Q. Wang).
 
10.03 Fabio Camilli (U. Roma "La Sapienza'') -  Stime di convergenza per l'omogenizzazione di equazioni nonlineari del secondo ordine

Dopo aver descritto brevemente l'approccio all'omogenizzazione di equazioni non lineari del secondo ordine mediante la teoria delle soluzioni viscosita', si discutono alcuni recenti risultati riguardanti stime sulla velocita' di convergenza della soluzione dell'equazione oscillante  alla soluzione del problema limite. In particolare si considerano sia il caso di una singola scala che il caso multiscala, inoltre l'effetto simultaneo dell'omogenizzazione e del vanishing viscosity.

17.03 Frank Pacard (Université Paris 12) -  Positive harmonic functions with 0 Dirichlet and constant Neumann boundary data

Are there any smooth domains in the plane supporting a positive harmonic function which has 0 Dirichlet boundary data and constant Neumann boundary data ? The half plane, the complement of a disc are obvious answers. I will show that there are also nontrivial examples. More generaly, we consider flat surfaces M with smooth boundary on which there exist positive harmonic functions having 0 Dirichlet data and constant Neumann data. I will show that this problem bear strong similarities with the study of minimal surfaces in Euclidean 3-space.

21.04 Hitoshi Ishii (Waseda University, Tokyo) - The Neumann problem for convex Hamilton-Jacobi equations in view of weak KAM

I will discuss a formula for the solutions of the Neumann problem for Hamilton-Jacobi equations. The discussion will be concerned with Aubry-Mather sets and optimal control of the associated Skorokhod problem, which the solution formula is based upon.

07.07 Salvador Moll (U. Valencia) - Rotationally symmetric 1-harmonic flows

15.07 Antonio Fasano (U. Firenze) - Modelling flows through porous hollow fibres