Quasiconvexity, (p,q)-growth and partial regularity

Franz Gmeineder (University of Konstanz) #

We display new results on the regularity properties of relaxed minimizers of quasiconvex functionals of \((p,q)\)-growth. These results apply to the natural range for which the functionals can be meaningfully extended (or relaxed) and apply to signed integrands as well. This extends previously known exponent ranges of Schmidt in a basically optimal way. Moreover, despite being natural in view of coercivity, signed, quasiconvex allow for different phenomena that are invisible in the convex situation. Specifically, some focus will be put on the non-availability of measure representations a la Fonseca & Maly for the relaxed functionals and, more importantly, why they are not really required for partial regularity.