A New Extension of Serrin's Lower Semicontinuity Theorem

2012/05/13 by Xiaohong, Hu, Shiqing, Zhang
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1205.2826

Abstract

In this paper, we present a new extension of the famous Serrin's lower semicontinuity theorem for the variational functional ∫_Ωf(x,u,u')dx,we prove its lower semicontinuity in W_loc^1,1(Ω) with respect to the strong L_loc¹ topology assuming that the integrand f(x,s,ξ) has the usual continuity on all the three variables and the convexity property on the variable ξ and the local absolute continuity on the variable x.

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