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$p$-Brownian motion and the $p$-Laplacian

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arxiv 2409.18744 v3 pith:GQKFJ7WF submitted 2024-09-27 math.PR math.AP

Viorel Barbu , Marco Rehmeier , Michael Röckner This is my paper · ORCID
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keywords brownianequationlaplacianmotionprocessclassicalconstructgiven
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abstract

In this paper we construct a stochastic process, more precisely, a (nonlinear) Markov process, which is related to the parabolic $p$-Laplace equation in the same way as Brownian motion is to the classical heat equation given by the (2-) Laplacian.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. McKean-Vlasov SDEs with Local Distributional Interactions: Well-Posedness and Entropy-Cost Estimates

    math.PR 2026-02 accept novelty 7.0 of 10

    McKean-Vlasov SDEs with distributional local negative-Sobolev kernels have global well-posedness from smoothed initial laws and entropy-cost estimates.

  2. The extended Dirichlet space and criticality theory for nonlinear Dirichlet forms

    math.FA 2025-01 accept novelty 7.0 of 10

    Nonlinear Dirichlet forms have an extended Dirichlet space, and their criticality and subcriticality are characterized by Hardy and Poincaré inequalities and by the norm of the constant function 1.

  3. McKean-Vlasov equations with singular coefficients - a review of recent results

    math.PR 2025-07 accept novelty 3.0 of 10

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  4. New perspectives on the d'Alembertian from general relativity. An invitation

    math.DG 2025-01 conditional novelty 2.0 of 10

    A review of the p-d'Alembertian framework for Lorentzian distance functions, giving distributional comparison theorems across the timelike cut locus.

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