The Alexandrov-Bakelman-Pucci Method and Its Applications

Daniele Castorina is Associate Professor of Mathematical Analysis at the Dipartimento di Matematica e Applicazioni “Renato Caccioppoli” of the Università degli Studi di Napoli Federico II. His research interests focus mainly on elliptic and parabolic partial differential equations. After graduating cum laude from Roma Tre University and obtaining his Ph.D. in Mathematics from Sapienza University of Rome, he was Lecturer in Mathematics at John Cabot University in Rome and held several postdoctoral positions at universities including Padua, Rome Tor Vergata, the Autonomous University of Barcelona, and Perugia.

Marco Casula is a PhD student in Mathematics at the University of Cagliari, enrolled in the XXXIX doctoral cycle under the supervision of Professors Andrea Loi and Roberto Mossa. His research focuses on complex and Kählerian geometry. Further research interests include Hermitian manifolds with torsion and the didactics of geometry. He has taken part in two visiting periods at the Universidade Estadual de Campinas under the supervision of Professor Henrique N. de Sá Earp, supported by INdAM funding and two Erasmus projects.

Alessandro Columbu is a mathematician and researcher specializing in Partial Differential Equations (PDEs). He is currently a postdoctoral researcher at the Department of Mathematics and Computer Science at the University of Cagliari, where he studies the role of PDEs in understanding natural phenomena under the supervision of Prof. Monica Marras. He received his Ph.D. in Mathematics and Computer Science with honors in February 2026. His doctoral thesis, supervised by Prof. Giuseppe Viglialoro, focused on structural conditions for global existence in chemotaxis systems. He also serves as an instructor and tutor for core courses, including Mathematical Analysis I & II, Geometry, and Algebra, at the Faculty of Engineering of the University of Cagliari.

Filippo Maria Cassanello is a PhD student in mathematics at the University of Cagliari. He earned his bachelor's and master's degrees in mathematics from the same university cum laude. His primary research interest is regularity theory for local and nonlocal elliptic and parabolic nonlinear operators. He also teaches contract courses for the University of Cagliari.