A1 Journal article (refereed)
Remarks on regularity for p-Laplacian type equations in non-divergence form (2018)

Attouchi, A., & Ruosteenoja, E. (2018). Remarks on regularity for p-Laplacian type equations in non-divergence form. Journal of Differential Equations, 265(5), 1922-1961. https://doi.org/10.1016/j.jde.2018.04.017

JYU authors or editors

Attouchi, Amal
Ruosteenoja, Eero

Publication details

All authors or editors: Attouchi, Amal; Ruosteenoja, Eero

Journal or series: Journal of Differential Equations

ISSN: 0022-0396

eISSN: 1090-2732

Publication year: 2018

Volume: 265

Issue number: 5

Pages range: 1922-1961

Publisher: Academic Press

Place of Publication: Maryland Heights

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jde.2018.04.017

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/58349

Abstract

We study a singular or degenerate equation in non-divergence form modeled on the p-Laplacian, −|Du|γ(Δu+(p−2)Δ∞ Nu)=finΩ. We investigate local C1,α regularity of viscosity solutions in the full range γ>−1 and p>1, and provide local W2,2 estimates in the restricted cases where p is close to 2 and γ is close to 0.

Keywords: partial differential equations; viscosity

Free keywords: p-Laplacian; viscosity solutions; local C1,α regularity; integrability of second derivatives

Fields of science: