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A New L 1 -Lower Semicontinuity Result

Daniele Graziani — 2007

Bollettino dell'Unione Matematica Italiana

The aim of this work is to prove a chain rule and an L 1 -lower semicontinuity theorems for integral functional defined on B V ( Ω ) . Moreover we apply this result in order to obtain new relaxation and Γ -convergence result without any coerciveness and any continuity assumption of the integrand f ( x , s , p ) with respect to the variable s .

Variational approximation for detecting point-like target problems

Gilles AubertDaniele Graziani — 2011

ESAIM: Control, Optimisation and Calculus of Variations

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.

Variational approximation for detecting point-like target problems

Gilles AubertDaniele Graziani — 2011

ESAIM: Control, Optimisation and Calculus of Variations

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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