Boundary Regularity for Fully Nonlinear Parabolic equations on C^1,Dini Domains

2025/08/11 by Xuemei Li, Dong, Jiqi, Li, Xuemei +2
Engineering · Mathematics · #35B30 #35B65 #35D40 #35K10 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.08008

openalex publication_date 2025/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the boundary pointwise Lipschitz regularity on exterior C^1,Dini domains and the Hopf lemma on interior C^1,Dini domains for fully nonlinear parabolic equations by a unified perturbation method. In fact, above two regularity hold for more general solution sets, i.e., the Pucci's class S^*(λ, Λ, f). Furthermore, based on the boundary pointwise Lipschitz regularity, we obtain the global W^2,δ regularity on exterior C^1,Dini domains for any 0<δ<1, which is new even for the harmonic functions.

Citations

• Boundary estimates for non-divergence equations in C¹ domains
• Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets
• Boundary pointwise regularity for fully nonlinear parabolic equations and an application to regularity of free boundaries
• Boundary pointwise regularity and applications to the regularity of free boundaries
• Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms
• Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary
• Pointwise regularity of the free boundary for the parabolic obstacle problem
• Boundary estimates for positive solutions to second order elliptic equations

Related

• Boundary pointwise regularity for fully nonlinear parabolic equations and an application to regularity of free boundaries
• Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations
• Boundary Pointwise C^1,α and C^2,α Regularity for Fully Nonlinear Elliptic Equations
• Borderline regularity for fully nonlinear equations in Dini domains
• C^{1, α}-regularity for solutions of degenerate/singular fully nonlinear parabolic equations