Interactions between

PDEs and Dynamical Systems


Working Group at

Università degli Studi di Torino

Dipartimento di Matematica

Upcoming Seminars

Davide Polimeni (Università di Torino)

15/05/2024, h. 14:30

Abstract: 

TBD

Past Seminars

Approximate symmetry for the Gidas-Ni-Nirenberg result in the unit ball 

17/04/2024, h. 14:30, Aula 5 (Palazzo Campana)

Abstract: 

In a celebrated paper published in 1979, Gidas, Ni & Nirenberg proved a symmetry result for a rigidity problem. With minimal hypotheses, the authors showed that positive solutions of semilinear elliptic equations in the unit ball are radial and radially decreasing.


This result had a big impact on the PDE community and stemmed several generalizations. In a recent work in collaboration with G. Ciraolo, M. Cozzi & M. Perugini this problem was investigated from a quantitative viewpoint, starting with the following question: given that the rigidity condition implies symmetry, is it possible to prove that if said condition is almost satisfied the problem is almost symmetrical?


With the employment of the method of moving planes and quantitative maximum principles we are able to give a positive answer to the question, proving approximate radial symmetry and almost monotonicity for positive solutions of the perturbed problem.

    Rotating spirals for three-component competition-diffusion systems

    20/03/2024, h. 11:00, Sala S (Palazzo Campana)

Abstract: 

We discuss the existence of rotating spirals for three-component competition-diffusion systems in B₁ ⊂ R², under the Neumann and the non-homogeneous Dirichlet boundary conditions. 

    Conformal and projective transformations on mechanical billiard systems 

    06/03/2024, h. 16.30, Aula 2 (Palazzo Campana)

Abstract: 

The integrability of free billiards in classical mechanics was first studied by G. D. Birkhoff, and later by Y. Sinai, their chaotic behavior and ergodicity were investigated. L. Boltzmann proposed planar billiard systems in the presence of a central force and predicted that such a billiard with a straight reflective wall that does not pass through the center would be ergodic. Recently, Gallavotti-Jauslion showed that under the Kepler potential, such billiards are not ergodic, but rather integrable. In this talk, we will show that conformal mappings can be used to relate various integrable billiard systems in the plane, including Boltzmann's integrable billiard system, and we will show that more general integrable billiard systems can be constructed under the Keplerian potential. Furthermore, by projective transformation, it is possible to obtain the corresponding integrable billiard systems on curved surfaces from these integrable billiard systems on the plane. This talk is based on collaborative research with Lei Zhao from the University of Augsburg. 

    Degenerate equations on nodal sets and boundary Harnack principles

    14/02/2024, h. 15.00, Sala S (Palazzo Campana)

Abstract: 

In this talk we present some elliptic equations whose coefficients

are degenerate on a nodal set of a given function. We also discuss applications to boundary Harnack principles.

    On the orbit determination problem for small bodies of the solar system

    30/01/2024, h. 14.30, Aula Lagrange (Palazzo Campana)

Abstract: 

The orbit determination (OD) problem for small bodies of the solar system, like asteroids, attracted the attention of famous mathematicians, as C.F. Gauss and P.-S. Laplace. After introducing the problem, their solutions will be briefly presented.

With the progress of technology and the realization of observation instruments more and more efficient, new mathematical challenges are arising. I will describe some recent initial OD methods that can help to process the huge amount of data produced by modern asteroid surveys. In my presentation I will focus especially on some algebraic aspects related to the proposed methods. 


    Discrete-to-Continuum Limits of Dynamical Optimal Transport Problems

     20/12/2023, h. 11.00, Aula Lagrange

     Abstract: link 


Regularity of the optimal sets for a class of integrals shape functionals

06/06/2023, h. 16.30, Aula Lagrange

Abstract: link


Spectral stability in domain with small holes

31/05/2023, h. 16.30, Sala S

Abstract: link


Nonlocal capillarity problems with anisotropic kernels

18/05/2023, h. 11.30, Aula 4

Abstract: link


Periodic solutions to relativistic Kepler problems

26/04/2023, h. 16.30, Sala S

Abstract: link


Chaos in Celestial Mechanics: applications to galactic billiards

28/03/2023, h. 14.30, Aula 3

Abstract: link


Oscillatory motions of the Restricted 3-body Problem: a functional analytic approach

23/03/2023, h. 15.30, Aula Magna

Abstract: link


Determinant of second variation

15/03/2023, h. 16.30, Sala S

Abstract: link


Chaotic phenomena to L_3 in the restricted 3-body problem

01/03/2023, h. 16.30, Sala S

Abstract: link


On critical points of solutions of semilinear elliptic problems

30/11/2022, h. 15.30, Sala S

Abstract: link


Regularity for the prescribed Lorentzian mean curvature equation, and the Born-Infeld model

24/11/2022, h. 15.00, Sala S

Abstract: link


Harmonic maps with free boundary and beyond

09/11/2022, h. 14.30, Sala S

Abstract: link


Dynamics & control of advanced space systems analysis, simulation, lab and flight experiments

30/09/2022, h. 10.30, Sala S

Abstract: link


Higher regularity of the free boundaries in obstacle problems

30/05/2022, h. 14:30, Aula 4

Abstract: link


Spectral stability, spectral flow and circular relative equilibria for the Newtonian N-body problem

24/05/2022, h. 14:30, Aula Lagrange

Abstract: link


Tori with prescribed almost constant mean curvature

18/05/2022, h. 14:30, Aula Lagrange

Abstract: link


Nodal length of random eigenfunctions and Wiener chaos

11/05/2022, h. 14:30, Aula Lagrange

Abstract: link


Maximal regularity for nonlinear mixed local and nonlocal problems

05/05/2022, h. 14:30, Aula Monod

Abstract: link


On the persistence of periodic tori for symplectic twist maps

26/04/2022, h. 14:30, Aula Lagrange

Abstract: link


Bubbles of prescribed mean curvature: an introduction

12/04/2022, h. 14:30, Aula Lagrange

Abstract: link


Arnold diffusion in the restricted planar elliptic three body problem

29/03/2022, h. 14:30, Sala S

Abstract: link

Università degli Studi di Torino

Dipartimento di Matematica

Palazzo Campana

via Carlo Alberto 10, 10123, Torino (TO)

Organizing Committee


Diego Berti

Irene De Blasi