Regularity of minimizers with generalized Orlicz growth

We will discuss the motivation of studying minimizers of  
variational integrals or solutions to partial differential equations  
with generalized Orlicz (also known as Musielak-Orlicz) growth  
conditions. After introducing the context, a global higher  
integrability result of the gradient of a minimizer related to an  
obstacle problem is shown. This talk is partly based on a joint work  
with Petteri Harjulehto and Peter Hästö.