Analysis of a variational model for motion compensated inpainting
Riccardo March Giuseppe Riey
Inverse Problems & Imaging 2017, 11(6): 997-1025 doi: 10.3934/ipi.2017046

We study a variational problem for simultaneous video inpainting and motion estimation. We consider a functional proposed by Lauze and Nielsen [25] and we study, by means of the relaxation method of the Calculus of Variations, a slightly modified version of this functional. The domain of the relaxed functional is constituted of functions of bounded variation and we compute a representation formula of the relaxed functional. The representation formula shows the role of discontinuities of the various functions involved in the variational model. The present study clarifies the variational properties of the functional proposed in [25] for motion compensated video inpainting.

keywords: Calculus of variations functional relaxation functions of bounded variations video inpainting optical flow estimation
One dimensional symmetry of solutions to some anisotropic quasilinear elliptic equations in the plane
Giuseppe Riey Berardino Sciunzi
Communications on Pure & Applied Analysis 2012, 11(3): 1157-1166 doi: 10.3934/cpaa.2012.11.1157
We prove one-dimensional symmetry of monotone solutions for some anisotropic quasilinear elliptic equations in the plane.
keywords: geometric analysis Degenerate anisotropic elliptic PDEs rigidity and symmetry results.

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