Speaker: José Miguel Urbano (KAUST and University of Coimbra)

Title: Regularity for nonlinear PDEs: from Hilbert’s 19th problem to intrinsic scaling

Abstract: The talk introduces intrinsic scaling, a powerful technique for analysing degenerate and singular PDEs. We highlight what is essential in the method and apply it to a model problem arising in phase transitions. We adopt a historical perspective, making a tour of regularity theory for nonlinear PDEs, from Hilbert’s 19th problem and the breakthroughs of De Giorgi and Nash in the 1950’s to the pioneering approach of DiBenedetto to degenerate equations.