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

Source 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 [Formula: see text] 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 C 1 -continuity assumptions with respect to the spatial variable x.