FALL 2020 Nonlinear Analysis Seminar Series

Bogdan Raita, Max Planck Institute for Mathematics in the Sciences

Title: Old and new in Compensated Compactness theory

Abstract:

We will review aspects of the theory of Compensated Compactness, starting with the fundamental work of Murat and Tartar and concluding with recent results obtained jointly with A. Guerra, J. Kristensen, and M. Schrecker. Broadly speaking, the object of this study is to gain a better understanding of the interaction between weakly convergent sequences and nonlinear functionals. The general framework will be that of variational integrals defined on spaces of vector fields satisfying linear pde constraints that satisfy Murat's constant rank condition. We will focus on the weak (lower semi-)continuity of these integrals, as well as the Hardy space regularity of the integrands.

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