Extremal spectral quantities and related problems


The purpose of this project is to combine analytic, geometric and computational techniques to study extremal values of different spectral quantities, such as individual eigenvalues, functions of these eigenvalues and some global spectral quantities. More specifically, some of the objects under consideration are the possible extremal sets of the first eigenvalue of the Laplacian with Robin boundary conditions, for which team members have recently shown that the ball is no longer an optimiser for large negative values of the boundary parameter, thus providing a counter-example to a 1977 conjecture, finite combinations of eigenvalues of the Laplace and Schrödinger operators, the functional determinant associated with these operators and the spectral abscissa of the (non self-adjoint) operator associated with the damped wave equation. To handle these problems a wide range of methods is required, including those from geometric analysis, functional analysis, control theory, numerical analysis, etc.

The host institution is the Group of Mathematical Physics of the University of Lisbon.

Time span: 15/05/2016-14/05/2019

Funding institution:  

Research team:

Some previous publications by group members

(for other relevant publications see the respective homepages)

Publications within the scope of this project

Project seminars

e-mail:psfreitas ( a@t )fc.ul.pt

Group of Mathematical Physics - University of Lisbon
Department of Mathematics
Faculty of Sciences
Campo Grande, Edifício C6
P-1749-016 Lisboa, Portugal