## Integral representation and relaxation for functionals defined on measures.(English)Zbl 0713.49018

Summary: Given a separable metric locally compact space $$\Omega$$, and a positive finite non-atomic measure $$\lambda$$ on $$\Omega$$, we study the ingegral representation on the space of measures with bounded variation $$\Omega$$ of the lower semicontinuous envelope of the functional $F(u)=\int_{\Omega}f(x,u)d\lambda \quad u\in L^ 1(\Omega,\lambda,{\mathbb{R}}^ n)$ with respect to the weak convergence of measures.

### MSC:

 49J45 Methods involving semicontinuity and convergence; relaxation