CAPDE   hosts  a group of researchers in  Nonlinear Analysis and Partial Differential Equations, affiliated to different universities in Chile, united by a broad history of joint collaboration. CAPDE intends to be  the umbrella to potentiate and disseminate our activity in research as well as that of our students, postdocs and collaborators.

Laplacian operator in the logo symbolizes the emphasis of our research in analysis of nonlinear PDEs of elliptic and parabolic type. These problems arise in models of many areas, among them  material science, astrophysics, combustion, superconductivity and supercooling theories, mathematical biology. On the other hand, understanding of these problems constitutes a powerful tool for other branches of mathematics, being for instance the analysis of singularities of a parabolic flow a key element in the proof of Poincaré´s conjecture. 

This mathematical field is  especially appealing  since its methods lie at the threshold of analysis, topology and geometry, with close contact to applied modelling. Nonlinear functional analysis, the calculus of variations, fine issues on linear PDE are at the core of this study, at the boundary of pure and applied mathematics.  Scientific computation has allowed to visualize complex phenomena, once unsuspected, whose mathematical understanding opens up formidable methodological challenges, so it does the increasing complexity of realistic models.   To this ultimate end, a deep understanding of simple form  classical problems is  an imperative,  often difficult task.