A-quasiconvexity and regularity

By Morrey’s foundational work, quasiconvexity displays a key notion in the vectorial Calculus of Variations. A suitable generalisation that keeps track of more elaborate differential conditions is given by Fonseca & Muller’s A-quasiconvexity. With the topic having faced numerous contributions as to lower semicontinuity, in this talk I give an overview of recent results for such problems with focus on the underlying function spaces and (partial) regularity. The talk is partially based on joint work with Sergio Conti (Bonn) and an ongoing project with Jan Kristensen (Oxford).