Remarks on regularity for p-Laplacian type equations in non-divergence\n form

2017/10/20 by Amal Attouchi, Attouchi, Amal, Eero Ruosteenoja +1 · 1 citation
Mathematics · #35B65 #35J60 #35J92 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1710.07506

openalex publication_date 2017/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a singular or degenerate equation in non-divergence form modeled by\nthe p-Laplacian, -|Du|^
gamma
left(
Delta u+(p-2)
Delta_
infty^Nν
right)=f




textin



Omega. We investigate local C^1,\α\nregularity of viscosity solutions in the full range \γ>-1 and p>1, and\nprovide local W^2,2 estimates in the restricted cases where p is close to\n2 and \γ is close to 0.\n

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• Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law

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