In the talk we introduce the so-called mean field planning problem: a coupled system of PDEs, a forward continuity equation and a backward Hamilton-Jacobi equation. The problem can be viewed as a modification of the mean field games system as well…
Categoria evento: Analysis Seminar
On the scaling limit of Onsager’s molecular model for liquid crystals – Yuning Liu (NYU University at Shanghai)
We study the small Deborah number limit of the Doi-Onsager equation for the dynamics of nematic liquid crystals. This is a Smoluchowski-type equation that characterizes the evolution of a number density function, depending upon both particle…
Optimal partitions. – Edouard Oudet (Centro De Giorgi)
Wepresentrecentnumericalapproachesdedicatedtotheidentification ofoptimalpartitionsassociatedtogeometricalcosts.Wefocusour presentationon2Dsurfacesandfull3Dproblems.…
Minimal Elastic Networks – Alessandra Pluda
In this talk we will consider planar networks of three curves minimizing a combination of the elastic energy and the length functional. We will prove existence and regularity of minimizers and we will show some properties of the minimal…
Functions of fractal bounded variation – Roger Züst
In this talk we introduce a notion of functions of fractal bounded variation. Here, the sup-norm of test functions as used in the classical definition is replaced by the Hoelder norm with respect to some exponent. Characteristic functions of domains…
Asymptotic planar N-bubble – Giacomo Del Nin (Universita’ di Pisa)
We consider in the plane a fixed finite number N of “bubbles”, that is disjoint finite perimeter sets which possibly share portions of their boundaries, and look for configurations that minimize, under a volume constraint, the total weighted length…
Branched transportation: stability and new models. – Andrea Marchese (University of Zurich)
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree, or the nervous and the cardiovascular systems. Given a flow that transports a…
A Hele-Shaw tumor growth model as a gradient flow. – Simone Di Marino (Scuola Normale Superiore)
In 2014 Perthame, Quiroz and Vasquez unite two types of modeling of tumor growth into a unique framework of reaction-diffusion type where the diffusive term is $\Delta p(\rho)$ and $p(\rho)=\rho^m$. The stiff limit $m \to \infty$ is in particular a…
On Aharonov-Bohm operators with moving poles – Veronica Felli (Università di Milano bicocca)
In this talk, I will present some results in collaboration with L. Abatangelo (Milano-Bicocca), L. Hillairet (Orléans), C. Léna (Torino), B. Noris (Amiens), M. Nys (Torino), concerning the behavior of the eigenvalues of Aharonov-Bohm operators with…
Liouville-type problems on compact surfaces: a variational approach – Aleks Jevnikar
A class of Liouville equations and systems on compact surfaces is considered: we focus on the Toda system which is motivated in mathematical physics by the study of models in non-abelian Chern-Simons theory and in geometry in the description of…