In 2017, it will be 40 years since the publication of Gilbarg and Trudinger’s Elliptic Partial Differential Equations of Second Order. We celebrate this with a program to link the past research with the future perspectives, by discussing what the important developments in the area during these forty years have been and what are the new trends of contemporary research. Particular attention will be given to some of the topics in which the book served as a great source of inspiration, such as fully nonlinear PDEs, viscosity solutions, Hessian equations, optimal transport, stochastic point of view, geometric flows, and so on.

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