On the first eigenvalue of Liouville-type problems

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Paolo Cosentino (Università di Roma II 'Tor Vergata')

Abstract: We are concerned with the spectrum of a linearized Liouville-type problem. Among other things, we characterize the case in which the first eigenvalue is zero. To this end, we refine the Alexandrov-Bol inequality suitable for our problem and characterize its equality case. As a consequence, we obtain new pointwise information on the first eigenfunction associated to the zero eigenvalue.