The paper is concerned with the analysis of a new variational model to restore point-like and curve-like singularities in biological images. To this aim we investigate the variational properties of a suitable energy which governs these pathologies. Finally in order to realize numerical experiments we minimize, in the discrete setting, a regularized version of this functional by fast descent gradient scheme.

We propose a new variational model to locate points in 2-dimensional biological images. To this purpose we introduce a suitable functional whose minimizers are given by the points we want to detect. In order to provide numerical experiments we replace this energy with a sequence of more treatable functionals by means of the notion of Γ-convergence.

Abstract. The aim of this paper is to provide a rigorous variational formulation for the detection of points in 2-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 Γ-convergence to the initial one.Mathematics Subject Classification. 49J45, 49Q20.

In this paper we address a relaxation theorem for a new integral functional of the calculus of variations defined on the space of functions in [Formula: see text] whose gradient is an Lp-vector field with distributional divergence given by a Radon measure. The result holds for integrand of type f(x, Δu) without any coerciveness condition, with respect to the second variable, and C1-continuity assumptions with respect to the spatial variable x.

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The aim of this work is to provide an L 1 -lower semicontinuity result for an integral convex functional defined on BV -vector valued functions, without any coerciveness and any continuity assumption on the integrand f (x, ξ) with respect to the variable x.

In the introduction ofIn subsection 2.3, problem (2.2) isIn section 6, problem (6.1) isIn subsection 6.3, problem (6.2) isThroughout the original paper the vector field U 0 is always given by −∇f , where f always denotes the solution of one of the problems (0.1), (0.2), (0.3), (0.4).In subsection 2

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