Applied Analysis Reading Group

20 February 2014: Nikolaos Katzourakis (Reading)

Vectorial Calculus of Variations in L∞ and Fully Nonlinear PDE Systems

In this talk I will discuss some results on the recently initiated field of vector-valued calculus of variations for supremal functionals and their relevant PDE system. The latter is the analogue of the Euler-Lagrange PDE in the space L∞. The simplest such system is the L∞-Laplacian. This highly nonlinear system is non-divergence and does not admit weak solutions in any standard sense. I will introduce some basics of a new PDE theory which allows to handle general fully nonlinear systems, and in particular the fundamental equations in L∞.

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