Gradient walk and p-harmonic functions

2016/05/18 by Hannes Luiro, Luiro, Hannes, Mikko Parviainen +1
Mathematics · #35J92 #60H30 #60J05 #60J60 #Acoustics #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Harmonic #Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Physics #math.AP #msc:35J92 #msc:60H30 #msc:60J05 #msc:60J60

paper · pdf · doi:10.48550/arxiv.1605.05564

arxiv created 2016/05/18 · openalex publication_date 2016/05/18 · arxiv updated 2016/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of stochastic processes and establish its connection to p-harmonic functions. In particular, we obtain stochastic approximations that converge uniformly to a p-harmonic function, with an explicit convergence rate, and also obtain a precise diffusion representation in continuous time. The main difficulty is how to deal with the zero set of the gradient of the underlying function.

Citations

• Elliptic Partial Differential Equations of Second Order
• C1 + α local regularity of weak solutions of degenerate elliptic equations

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