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

2025/11/10 by Claudemir Alcantara, Alcantara, Claudemir, Makson S. Santos +1
Mathematics · #35B65 #35D40 #35J60 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2511.07356

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/31

Abstract

We examine the interior regularity of solutions to a degenerate normalized p-Laplace equation, where the degeneracy is governed by a modulus of continuity whose inverse satisfies a Dini continuity condition. We prove that under very general assumptions on the degeneracy law, solutions belong to the C¹ class. We argue by approximating the solutions by a sequence of hyperplanes, which allows us to prove the desired regularity.

Citations

• Regularity estimates for quasilinear elliptic PDEs in non-divergence form with Hamiltonian terms and applications
• Geometric regularity estimates for quasi-linear elliptic models in non-divergence form with strong absorption
• Interior regularity estimates for fully nonlinear equations with arbitrary nonhomogeneous degeneracy laws
• Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations
• Differentiability of solutions for a degenerate fully nonlinear free transmission problem
• Regularity of solutions to degenerate normalized p-Laplacian equation with general variable exponents
• C¹-regularity for degenerate diffusion equations
• Gradient regularity for a singular parabolic equation in non-divergence form
• Gradient continuity estimates for the normalized p-Poisson equation
• Remarks on regularity for p-Laplacian type equations in non-divergence\n form
• C^1,α regularity for the normalized p-Poisson problem
• Hölder gradient estimates for parabolic homogeneous p-Laplacian equations
• Local regularity results for value functions of tug-of-war with noise and running payoff
• Harnack's inequality for p-harmonic functions via stochastic games
• Regularity for radial solutions of degenerate fully nonlinear equations
• On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian
• Tug of war with noise: a game theoretic view of the p-Laplacian

Related

• Regularity of solutions to degenerate normalized p-Laplacian equation with general variable exponents
• Regularity of solutions to degenerate p-Laplacian equations
• C¹-regularity for degenerate diffusion equations
• Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations
• C^{1, α}-regularity for functions in solution classes and its application to parabolic normalized p-Laplace equations