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Relaxation for a class of nonconvex functionals defined on measures. (English) Zbl 0791.49016

Summary: We characterize in a suitable integral form like \[ \overline F(\lambda)= \int_ \Omega\overline f\left(x, {d\lambda\over d\mu}\right) d\mu+ \int_{\Omega\backslash A_ \lambda} \overline\varphi(x,\lambda^ s)+ \int_{A_ \lambda} \overline g(x,\lambda(x))d\# \] the lower semicontinuous envelope \(\overline F\) of functionals \(F\) defined on the space \({\mathcal M}(\Omega;{\mathbf R}^ n)\) of all \({\mathbf R}^ n\)-valued measures with finite variation on \(\Omega\).

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
46G10 Vector-valued measures and integration
46E27 Spaces of measures
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References:

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