Differential Equations and Numerical Analysis Seminar - 20/06/2012

Wednesday, 20 June 2012, 3:00 p.m.

Lecturer: Alessandro Portaluri, Università del Salento (Lecce - Itália)

Title: "Morse-Smale index theorems for elliptic boundary deformation problems".

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: We prove a Morse-Smale index theorem for a second order self-adjoint elliptic boundary value problem in divergence form on a star-shaped domain of the N-dimensional Euclidean space with Dirichlet and Neumann boundary conditions. In particular, we show the equality of the Maslov index with the generalized Morse index defined as the spectral flow of a family of self-adjoint operators related to the variational formulation of a one-parameter family of boundary deformation problems. We employ and generalize the idea of shrinking the boundary recently introduced by Deng-Jones, by reformulating the trace map in a proper symplectic context.
(This is a joint work with Francesca Dalbono).