Carriero, Michele; Leaci, Antonio; Pascali, Eduardo Integrals with respect to a Radon measure added to area type functionals: semi-continuity and relaxation. (English) Zbl 0632.49005 Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 78, 133-137 (1985). In this expository note the authors present some results for integral functionals of the type \[ F(u)=\int_{\Omega}f(x,u,Du)dx+\int_{{\bar \Omega}}g(x,u)d\mu I=I(u)+\int_{\Omega}g(x,u)d\mu. \] In particular, under the assumption that I is \(L_ 1(\Omega)\)-lower semicontinuous, they present a result on the \(L_ 1(\Omega)\)-lower semicontinuity of F over \(W^{1,1}(\Omega)\cap C^ 0({\bar \Omega})\) and a result on the integral representation of the relaxed functional in the following terms: \(sc^-(L_ 1(\Omega))F=I(u)+\int_{\Omega}\gamma (x,u)d\mu\). Reviewer: A.Salvadori Cited in 1 Document MSC: 49J45 Methods involving semicontinuity and convergence; relaxation 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures 49M20 Numerical methods of relaxation type Keywords:integral functionals; semicontinuity; relaxed functional PDFBibTeX XMLCite \textit{M. Carriero} et al., Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 78, 133--137 (1985; Zbl 0632.49005)