Unified approach to C^1,α regularity for quasilinear parabolic equations

2020/09/04 by Karthik Adimurthi, Adimurthi, Karthik, Agnid Banerjee +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.02227

openalex publication_date 2020/09/04 · openalex created_date 2023/02/21 · openalex updated_date 2026/07/28

Abstract

In this paper, we are interested in obtaining a unified approach for C^1,α estimates for weak solutions of quasilinear parabolic equations, the prototype example being u_t - div (|∇ u|^p-2 ∇ u) = 0. without having to consider the singular and degenerate cases separately. This is achieved via a new scaling and a delicate adaptation of the covering argument developed by E.~DiBenedetto and A.~Friedman.

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