On the lower semicontinuous envelope of functionals defined on polyhedral chains
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We prove that solutions of a mildly regularized Perona–Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the gener ...
Some new results are presented concerning the search and approximation of solutions of equations in metric spaces using functionals strictly subordinated to a convergent series and functionals compatible with a convergent series. These classes of functiona ...
We adopt an innovation-driven framework and investigate the sparse/compressible distributions obtained by linearly measuring or expanding continuous-domain stochastic models. Starting from the first principles, we show that all such distributions are neces ...
We consider the long time behavior of the semidiscrete scheme for the Perona-Malik equation in one dimension. We prove that approximated solutions converge, in a slow time scale, to solutions of a limit problem. This limit problem evolves piecewise constan ...
The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time a(n ...
We investigate how various treatments of exact exchange affect defect charge transition levels and band edges in hybrid functional schemes for a variety of systems. We distinguish the effects of long-range vs short-range exchange and of local vs nonlocal e ...
We prove that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows us to characterize also minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional. ...
Orbital-density-dependent functionals, such as the Perdew-Zunger or the Koopmans-compliant functionals, are used to remove unphysical self-interaction energies and to restoremissing piece-wise linearity in approximate formulations of density-functional the ...
Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, ...
We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and pr ...