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

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.