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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

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

Viorel Barbu , Marco Rehmeier , Michael R\"ockner This is my paper
classification math.PR math.AP
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 2 Pith papers

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  1. Brownian motion in Minkowski normed spaces

    math.PR 2026-07 unverdicted novelty 7.0

    Constructs a pathwise-unique strong solution to a singular McKean-Vlasov SDE whose marginal laws are the fundamental solutions of the nonlinear Finsler heat equation on Minkowski normed spaces.

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

    math.PR 2026-02 accept novelty 7.0

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