Analysis Seminar @CMUC (Center for Mathematics of the University of Coimbra)
There will be two speakers, the duration of each
talk is approximately 40 min, thus the session
should finish at 15.50, twenty minutes later than usual.
The attached .pdfs contain extended abstracts with references, etc.
Speaker 1: Gabrielle Terrone, IST
Title: Bernstein estimates for systems of weakly coupled fully non-linear elliptic equations and integral operators.
Abstract: Bernstein estimates permit to bound the sup-norm of the gradient of the solution with the sup-norm of the solution. We are particularly interested in systems that arise in the stochastic optimal control problems of hybrid systems, that are systems of weakly coupled nonlinear elliptic equations. Our techniques can also be adapted to handle nonlocal integral operators, such as the factional Laplacian. In both cases, a generalization of Bernstein estimates for first and second derivatives of classical solutions will be presented. In the light of the approach of Caffarelli-Cabré, Bernstein estimates follow rather simply from the maximum principle for the associated linearized operator.
This is a joint work with Diogo Gomes.
Speaker 2: Filippo Cagnetti, IST
Title: Non Convex Aubry-Mather Measures
Abstract: Given a smooth Hamiltonian H, we study the existence of measures invariant under the Hamiltonian flow, when H is non-convex. To simplify the treatment, we restrict ourselves to the periodic setting. Due to the lack of convexity, it is not possible to pass to the Lagrangian formulation,
and to use the classical variational approach.
Instead, we apply the “Adjoint method” recently developed by Evans.
This is a joint work with Diogo Gomes, IST, Lisbon,
and Hung V. Tran, University of California, Berkeley.
Date: April, 9 (Friday), 14h30.