Higher regularity estimates for solutions to ∞-Laplacian-type models

2025/04/26 by da Silva, João Vitor, Santos, Makson S., Soares, Mayra
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.18994

Abstract

In this work, we tackle the higher regularity estimates of solutions to inhomogeneous ∞-Laplacian equations at interior critical points. Our estimates provide smoothness properties better than the corresponding available regularity for the model with bounded forcing terms. We explore several scenarios, thereby obtaining improved regularity estimates, which depend on the universal parameters of the model. Our findings connect with nowadays well-known estimates developed for obstacle and dead-core type problems.

Citations

• Sharp and improved regularity estimates for weighted quasilinear elliptic equations of p-Laplacian type and applications
• Higher regularity of solutions to fully nonlinear elliptic equations
• Regularity in the two-phase Bernoulli problem for the p-Laplace operator
• Liouville theorems for infinity Laplacian with gradient and KPP type\n equation
• Regularity properties for p-dead core problems and their asymptotic limit as p → ∞
• Regularity properties for p−dead core problems and their asymptotic limit as p→∞
• Sharp regularity estimates for quasi-linear elliptic dead core problems and applications
• Sharp regularity estimates for quasi-linear elliptic dead core problems and applications
• Regularity for the fully nonlinear dead-core problem
• Infinity Laplacian equation with strong absorptions
• Optimal regularity at the free boundary for the infinity obstacle problem
• Inhomogeneous Dirichlet problems involving the infinity-Laplacian
• An easy proof of Jensen’s theorem on the uniqueness of infinity harmonic functions
• Tug-of-war and the infinity Laplacian
• Regularity of a free boundary with application to the Pompeiu problem

Related

• Higher regularity of solutions to fully nonlinear elliptic equations
• Improved regularity estimates for Hardy-Hénon-type equations driven by the ∞-Laplacian
• Regularity properties for p-dead core problems and their asymptotic limit as p → ∞
• Remarks on regularity for p-Laplacian type equations in non-divergence\n form
• Regularity properties for p−dead core problems and their asymptotic limit as p→∞