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Seminario de Ecuaciones Diferenciales: «On the first eigenvalue of liouville-type problems»

Seminario a cargo de Paolo Cosentino (Università di Roma II ‘Tor Vergata’)

Resumen: 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.