A New Extension of Serrin's Lower Semicontinuity Theorem

Abstract EN

We present a new extension of Serrin's lower semicontinuity theorem.

We prove that the variational functional ∫Ωfx,u,u′dx defined on Wloc1,1Ω is lower semicontinuous with respect to the strong convergence in Lloc1, under the assumptions that the integrand fx,s,ξ has the locally absolute continuity about the variable x.