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Existence of infinitely many solutions for the one-dimensional Perona-Malik model

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Abstract

We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem.

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  1. Department of Mathematics, University of Sussex, Brighton, BN1 9R, UK

    Kewei Zhang

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  1. Kewei Zhang
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Zhang, K. Existence of infinitely many solutions for the one-dimensional Perona-Malik model. Calc. Var. 26, 171–199 (2006). https://doi.org/10.1007/s00526-005-0363-4

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  • DOI: https://doi.org/10.1007/s00526-005-0363-4

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