On coercive variational integrals

It is well-known that sequential weak lower semicontinuity of a variational integral F(u,Ω)=∫ΩF(∇u(x))dx on the Sobolev space W1,p(Ω,RN) under a p-growth condition on the integrand F is equivalent to quasiconvexity in the sense of Morrey. We show that coercivity on Dirichlet classes likewise is equivalent to a quasiconvexity condition. We also discuss some examples and extend a sequential weak lower semicontinuity result to the case of signed integrands.