We give a complete classification of the stability properties of the equilibria for the semi-discrete one-dimensional Perona-Malik equation, with Dirichlet boundary conditions. We also give the $\Gamma$-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.
Paolini, M., Bellettini, G., Novaga, M., Classification of the equilibria for the semi-discrete Perona-Malik equation, <<CALCOLO>>, 2009; 46 (Dicembre): 221-243. [doi:10.1007/s10092-009-0006-9] [http://hdl.handle.net/10807/11577]
Classification of the equilibria for the semi-discrete Perona-Malik equation
Paolini, Maurizio;Bellettini, Giovanni;Novaga, Matteo
2009
Abstract
We give a complete classification of the stability properties of the equilibria for the semi-discrete one-dimensional Perona-Malik equation, with Dirichlet boundary conditions. We also give the $\Gamma$-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.
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