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

Abstract: The talk is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs. We bring to light what is essential in the method and develop an application to a model arising in phase transitions. We follow an historical perspective, making a tour of regularity theory for nonlinear PDEs, from Hilbert’s 19th problem and the breakthroughs of DeGiorgi and Nash to the contributions of the Russian school and the pioneering approach of DiBenedetto to degenerate equations.