The Infinity Laplacian (Session I)

Overview

Abstract

The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.

Brief Biography

José Miguel Urbano is a Professor of Mathematics at the University of Coimbra (Portugal). He holds a Ph.D. from the University of Lisbon and did a postdoc at Northwestern University in Chicago. He is the author of the book The Method of Intrinsic Scaling and of over 50 scientific papers in the area of Nonlinear Partial Differential Equations. He has supervised four Ph.D. students and ten postdoctoral fellows. He was a member of the Scientific Council for the Exact Sciences and Engineering of the Portuguese Science Foundation (FCT) and has served as an evaluator of grants and research projects for the EU (Marie-Curie Fellowships), ERC (Starting Grants), the Academy of Finland, the Latvian Council of Science and FCT. He has taught short courses at IMPA (Rio de Janeiro, Brazil), the University of Florence (Italy), Aalto University (Finland), the Federal University of Ceará (Fortaleza, Brazil), KAUST (Saudi Arabia), and Seoul National University (South Korea). He is a Corresponding Academician of the Sciences Class (Mathematics Section) of the Lisbon Academy of Sciences.