Final Report Summary - VECTORIAL PROBLEMS (Vectorial Elliptic, Parabolic and Variational Problems: Singularities and Regularity)
The project has exploited basic properties of singular sets of vectorial problems, both in the interior and in the boundary case. Moreover, nonlinear potential techniques have been introduced in order to study the fine pointwise behavior of solutions to nonlinear elliptic and parabolic equations and systems. New gradient estimates for solutions in terms of linear and nonlinear potentials have been discovered. These allow to control regularity and singularities of solutions. Their use allows to determine sharp regularity criteria, leading to the solution of longstanding open issues in regularity theory.