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A RELAXATION RESULT FOR AN INHOMOGENEOUS FUNCTIONAL PRESERVING POINT-LIKE AND CURVE-LIKE SINGULARITIES IN IMAGE PROCESSING

GILLES AUBERT

Laboratoire J. A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose 06108 Nice Cedex 2, France

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DANIELE GRAZIANI

Morpheme CNRS/INRIA/UNSA Sophia Antipolis, Inria, 2004 route des Lucioles, BP 93 06902 Sophia Antipolis Cedex, France

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https://doi.org/10.1142/S0129167X12501200Cited by:1 (Source: Crossref)

Abstract

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 whose gradient is an L^p-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.

Keywords:

AMSC: 49J45, 49M20, 49Q20

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