Regularity of solutions to degenerate normalized p-Laplacian equation with general variable exponents

2023/03/02 by Wang, Jiangwen, Yin, Yunwen, Jiang, Feida · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.01190

Abstract

In this paper, we consider a kind of degenerate normalized p-Laplacian equation with general variable exponents. We establish local C^1,α' regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise C^1,τ regularity for degenerate free transmission problem related to normalized p-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis.

Cited by

• Regularity for fully nonlinear degenerate parabolic equations with strong absorption
• Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law

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