Double phase functionals and approximation

The talk shall introduce double-phase functionals and spaces,
and discuss their approximation properties. The spaces of our interest
are inhomogeneous Sobolev-type spaces, which lie between classical
Sobolev spaces. We shall see that regular functions are not always dense
in such spaces, and discuss results on when the density occurs, and when
it does not. This is joint work with Iwona Chlebicka, Filomena De
Filippis, and Błażej Miasojedow.