On regularity of the time derivative for degenerate parabolic systems

2015/01/20 by Jens Frehse, Frehse, Jens, Sebastian Schwarzacher +1
Computer Science · Engineering · Mathematics · #35B45 #35K40 #35K65 #35Q35 #76D07 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1501.04876

openalex publication_date 2015/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) p-Laplace system and models for non Newtonien fluids of powerlaw or Carreau type. By the use of special weak different quotients, adapted to the variational structure we bound fractional derivatives of u_t in time and space direction. Although the estimates presented here are valid under very general assumptions they are a novelty even for the parabolic p-Laplace equation.

Citations

• Everywhere regularity of functionals with φ-growth

Related

• Time derivative estimates for parabolic p-Laplace equations and applications to optimal regularity
• Further time regularity for fully non-linear parabolic equations
• Regularity of Solutions of the Parabolic Normalized p-Laplace Equation
• Regularity for Fully Nonlinear P-Laplacian Parabolic Systems: the Degenerate Case
• Further Time Regularity for Non-Local, Fully Non-Linear Parabolic\n Equations