The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
José Miguel Urbano is a Professor of Mathematics at the University of Coimbra (Portugal). He holds a PhD 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 PhD 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 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.