27 citations · 69 across the 10 of their papers we have counts for
12 papers
Conformal Parametrisation of Star-Shaped Domains and Persistence of Semilinear Elliptic Solutions
Gianni Arioli
We study the conformal parametrisation of smooth star-shaped planar domains and its dependence on perturbations of the boundary. The boundary correspondence of the normalized Riema…
Some bounds for the eigenfunctions of the Stokes problem under Navier boundary conditions in a cube
Gianni Arioli, Alessio Falocchi, Filippo Gazzola
We prove some bounds for the eigenfunctions of the Stokes problem under Navier boundary conditions in a cube.
Computer assisted proof of branches of stationary and periodic solution, and Hopf bifurcations, for dissipative PDEs
Gianni Arioli
We discuss an approach to the computer assisted proof of the existence of branches of stationary and periodic solutions for dissipative PDEs, using the Brussellator system with dif…
A Hopf bifurcation in the planar Navier-Stokes equations
Gianni Arioli, Hans Koch
We consider the Navier-Stokes equation for an incompressible viscous fluid on a square, satisfying Navier boundary conditions and being subjected to a time-independent force. As th…
Traveling wave solutions for the FPU chain: a constructive approach
Gianni Arioli, Hans Koch
Traveling waves for the FPU chain are constructed by solving the associated equation for the spatial profile of the wave. We consider solutions whose derivatives need not…
A model for stocks dynamics based on a non-Gaussian path integral
Giovanni Paolinelli, Gianni Arioli
We introduce a model for the dynamics of stock prices based on a non quadratic path integral. The model is a generalization of Ilinski's path integral model, more precisely we choo…
Some breathers and multi-breathers for FPU-type chains
Gianni Arioli, Hans Koch
We consider several breather solutions for FPU-type chains that have been found numerically. Using computer-assisted techniques, we prove that there exist true solutions nearby, an…
A path integral based model for stocks and order dynamics
Giovanni Paolinelli, Gianni Arioli
We introduce a model for the short-term dynamics of financial assets based on an application to finance of quantum gauge theory, developing ideas of Ilinski. We present a numerical…
Validated numerical solutions for some semilinear elliptic equations on the disk
Gianni Arioli, Hans Koch
Starting with approximate solutions of the equation on the disk, with zero boundary conditions, we prove that there exist true solutions nearby. One of the challenges he…
Torsional instability in suspension bridges: the Tacoma Narrows Bridge case
Gianni Arioli, Filippo Gazzola
All attempts of aeroelastic explanations for the torsional instability of suspension bridges have been somehow criticised and none of them is unanimously accepted by the scientific…
On a nonlinear nonlocal hyperbolic system modeling suspension bridges
Gianni Arioli, Filippo Gazzola
We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth orde…
Periodic orbits, symbolic dynamics and topological entropy for the restricted 3-body problem
Gianni Arioli
This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existe…