2013/09/27 by Verena Bögelein · 13 citations
Mathematics · #Balanced flow #Boundary (topology) #Boundary value problem #Geometric Analysis and Curvature Flows #Lipschitz continuity #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Parabolic partial differential equation #math.AP
paper · pdf · doi:10.1112/plms/pdv027
published in Proceedings of the London Mathematical Society 111(3), 633-680 (Wiley)
arxiv created 2013/09/27 · openalex publication_date 2015/08/04 · openalex created_date 2016/06/24 · arxiv updated 2017/05/17 · openalex updated_date 2026/08/05
A by now classical result due to DiBenedetto states that the spatial gradient of solutions to the parabolic p-Laplacian system is locally H"older continuous in the interior. However, the boundary regularity is not yet well understood. In this paper we prove a boundary L^∞-estimate for the spatial gradient Du of solutions to the parabolic p-Laplacian system ∂t u - \Div (|Du|p-2Du) = 0 \quadin Ω×(0,T) for p≥ 2, together with a quantitative estimate. In particular, this implies the global Lipschitz regularity of solutions. The result continues to hold for the so called asymptotically regular parabolic systems.