Abstract: The theory of regularity, beyond its theoretical relevance in the study of partial differential equations, plays a central role in modeling various natural phenomena, including those arising in biology, materials science, fluid dynamics, and mathematical physics.
In this talk, we will present results concerning the regularity of solutions to equations governed by the infinity Laplacian, with particular emphasis on infinity-harmonic functions, as well as recent advances on singular problems and Hénon-type equations.