The aim of this work is to prove a chain rule and an -lower semicontinuity theorems for integral functional defined on . Moreover we apply this result in order to obtain new relaxation and -convergence result without any coerciveness and any continuity assumption of the integrand with respect to the variable .
The aim of this paper is to provide a rigorous variational formulation for the detection of points in -d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the -convergence to the initial one.
The aim of this paper is to provide a rigorous variational formulation for the detection of points in -d biological images. To this purpose we introduce a new functional whose minimizers give the points we want to detect. Then we define an approximating sequence of functionals for which we prove the -convergence to the initial one.
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