Introducing the p-Laplacian Spectra

Abstract : In this work we develop a nonlinear transform, associated with nonlin-ear eigenfunctions of the p-Laplacian for p ∈ (1, 2). This bridges the gap between the Fourier transform (p = 2) and the recently proposed Total Variation (TV) transform (p = 1). We first analyze the behavior of nonlinear eigenfunctions of the p−Laplacian under the p−Laplacian flow. We provide an analytic solution and show finite extinction time. A main innovation of this study is concerned with operators of fractional homogeneity which require the mathematical framework of fractional calculus. The proposed p-Laplacian transform rigorously defines the notions of decomposition, reconstruction, filtering and spectrum. Although the study is focused on the p-Laplacian operator, the mathematical results are valid for any homogeneous operator of order in the range of (0, 1).
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https://hal.archives-ouvertes.fr/hal-02085700
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Submitted on : Thursday, August 8, 2019 - 12:00:46 AM
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  • HAL Id : hal-02085700, version 2

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Ido Cohen, Guy Gilboa. Introducing the p-Laplacian Spectra. 2019. ⟨hal-02085700v2⟩

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