Giorgio Fusco, Università dell Aquila
Equivariant entire solutions to elliptic
systems with variational structure
Thursday, November 19 2009, at 15:00
Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, aula 3014 edificio U5 III piano | |
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Bernard Helffer, Université de Paris XI
On Nodal domains and spectral minimal partitions: new results and open problems
Monday, October 26 2009, at 17:00
Università di Milano-Bicocca, Dipartimento di Matematica e Applicazioni, aula 45 II piano |
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Abstract
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Given a bounded open set $\Omega$
in $\mathbb{R}^2$ or in a Riemannain manifold
and a partition of $\Omega$
by $k$ open sets $\omega_j$ , we can consider the quantity
$\max_j \lambda(\omega_j)$ where $\lambda(\omega_j)$ is the ground state energy of
the Dirichlet realization of the Laplacian in $\omega_j$. If we denote by
$\mathcal{L}_k(\Omega
)$ the infimum over all the $k$-partitions of
$\max_j \lambda(\omega_j)$, a minimal $k$-partition is then a partition which
realizes the infimum.
Although the analysis is rather standard when $k=2$ (we find the nodal domains of a second
eigenfunction), the analysis of higher $k$ becomes non trivial and quite interesting.
In this talk, we would like to discuss the properties of minimal spectral partitions,
illustrate the difficulties by considering simple cases like the disc, the rectangle
or the sphere ($k = 3$) and also exhibit the possible role of the hexagone in the
asymptotic behavior as $k \to \infty$ of
$\mathcal{L}_k(\Omega
)$. We will also explain the link of these questions with spectral
properties of some Aharonov-Bohm hamiltonians.
We will finally discuss other definitions of minimal partitions.
This work has started in collaboration with T. Hoffmann-Ostenhof and has been continued
(published or to appear) with the coauthors V. Bonnaillie-Noel, T. Hoffmann-Ostenhof, S. Terracini
and G. Vial. |
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Wei-Min Wang, Université Paris-Sud
Spectral method in Hamiltonian PDE
Monday, October 12 2009, at 17:30
Dipartimento di Matematica, Universita di Milano | |
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Jun-Cheng Wei, The Chinese University of Hong Kong
On De Giorgi Conjecture and Beyond
Friday, October 02 2009, at 15:00
TBA | |
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Neil Trudinger, Australian National University
Optimal Transportation in the 21st century
Tuesday, September 29 2009, at 16:30
Dipartimento di Matematica, Università di Milano - Via Saldini 50, Aula Chisini | |
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Eduard Feireisl, Mathematical Institute, Czech Academy of Sciences
Asymptotic analysis in thermodynamics of viscous fluids
Monday, September 21 2009, at 17:30
Dipartimento di Matematica, Politecnico di Milano, Aula Consiglio VII piano | |
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