Gradient regularity for a class of doubly nonlinear parabolic partial differential equations

2024/07/08 by Michael Strunk, Strunk, Michael
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2407.05631

openalex publication_date 2024/07/08 · openalex created_date 2024/07/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the local gradient regularity of non-negative weak solutions to doubly nonlinear parabolic partial differential equations of the type ∂_t u^q - div A(x,t,Du)=0 \qquadin Ω_T, with q>0, Ω_T=Ω×(0,T)⊂ℝⁿ⁺¹ a space-time cylinder, and A=A(x,t,ξ) a vector field satisfying standard p-growth conditions. Our main result establishes the local Hölder continuity of the spatial gradient of non-negative weak solutions in the super-critical fast diffusion regime 0

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