ABP estimate and Harnack inequality for a class of degenerate fully nonlinear pseudo-p-Laplacian equations

2025/09/29 by Sun‐Sig Byun, Byun, Sun-Sig, Hongsoo Kim +1
Computer Science · Mathematics · #35B65 #35D40 #35J15 #35J70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2509.24442

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We prove Aleksandrov-Bakelman-Pucci estimates and Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear pseudo-p-Laplacian equations in nondivergence form. Our main approach is an adaptation of the sliding paraboloid method with anisotropic functions tailored to the coordinatewise degeneracy.

Citations

• A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
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• Lipschitz regularity for local minimizers of some widely degenerate problems
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• Small Perturbation Solutions for Parabolic Equations

Related

• Harnack inequality for degenerate fully nonlinear parabolic equations
• Harnack estimates for quasi-linear degenerate parabolic differential equations
• Harnack inequality for degenerate and singular operators of p-Laplacian type on Riemannian manifolds
• Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds
• Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate Case