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Classification of equilibria and Γ-convergence for the discrete Perona-Malik functional

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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 Γ-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133, Rome, Italy

    G. Bellettini & C. Tornese

  2. INFN Laboratori Nazionali di Frascati, via E. Fermi 40, 00044, Frascati, Rome, Italy

    G. Bellettini

  3. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    M. Novaga

  4. Dipartimento di Matematica e Fisica, Università Cattolica di Brescia, via Trieste 41, 25121, Brescia, Italy

    M. Paolini

Authors
  1. G. Bellettini
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  2. M. Novaga
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  3. M. Paolini
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  4. C. Tornese
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Corresponding author

Correspondence to M. Paolini.

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Bellettini, G., Novaga, M., Paolini, M. et al. Classification of equilibria and Γ-convergence for the discrete Perona-Malik functional. Calcolo 46, 221–243 (2009). https://doi.org/10.1007/s10092-009-0006-9

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  • DOI: https://doi.org/10.1007/s10092-009-0006-9

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