Martedì 15 Gennaio 2025 ore 15.00 Aula di Consiglio (Sala Professori I livello DMA)

Seminario di Analisi

Antonio Iannizzotto (Università di Cagliari)

A DIFFERENT APPROACH TO REGULARITY FOR THE FRACTIONAL p-LAPLACIAN

The fractional p-Laplacian is the model case of divergence-form  nonlinear, nonlocal operators, which have attracted increasing  attention in recent years, especially within the field of regularity  theory. It is well known, since the 2016 work of Di  Castro-Kuusi-Palatucci, that weak solutions of the fractional  p-Laplace equation are locally Hölder continuous. I will present a new  proof of such result, obtained in collaboration with F. Cassanello,  F.G. Düzgün, and V. Vespri, based on the method of positivity  clustering and expansion introduced by DiBenedetto, and discuss some  developments and applications.