Workshop on Nonlinear Parabolic PDEs
11 June - 15 June 2018
A crucial role in understanding nonlinear phenomena is played by regularity estimates based only on the structure of the equation. Indeed, solutions of nonlinear PDEs, when they exist, are not smooth. Over the last few decades a vast amount of research papers have been published and powerful techniques have been developed to understand these phenomena. Recent advances, some of which by participants in the workshop, have already turned out to be powerful enough to solve several previously unreachable problems and have opened up a whole new area of research. This workshop will focus on three themes related to nonlinear parabolic PDEs which have gained traction recently: Boundary regularity, with the goal to discuss and provide a Wiener criterion for a wide class of nonlinear parabolic PDEs. Nonlinear thermal capacity, with the goal to discuss and develop a nonlinear capacity theory for a wide class of nonlinear parabolic PDEs. Gradient estimates, with the goal to discuss and extend higher integrability results of the gradient for a wide class of nonlinear parabolic PDEs.
University of Salzburg