Lower semicontinuity of integrals of the calculus of variations in Cheeger-Sobolev spaces

摘要

A necessary condition called H 1, p mu -quasiconvexity on p-coercive integrands is introduced for the lower semicontinuity with respect to the strong convergence of L p mu ( X; Rm) of integral functionals defined on Cheeger-Sobolev spaces. Under polynomial growth conditions it turns out that this condition is necessary and sufficient.