On coercive variational integrals. (April 2017) - Chen, Chuei Yee; Kristensen, Jan
Abstract: It is well-known that sequential weak lower semicontinuity of a variational integral F ( u, Ω ) = ∫ Ω F ( ∇ u ( x ) ) d x on the Sobolev space W 1, p ( Ω, R N ) 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.