Unified approach to $C^{1,\alpha}$ regularity for quasilinear parabolic equations

Adimurthi; Agnid Banerjee

doi:10.4171/rlm/990

JournalsrlmVol. 33, No. 4pp. 833–883

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

Adimurthi
Tata Institute of Fundamental Research, Bangalore, India
Agnid Banerjee
Tata Institute of Fundamental Research, Bangalore, India

$Unified approach to $C^{1,\alpha}$ regularity for quasilinear parabolic equations cover$

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Abstract

In this paper, we are interested in obtaining a unified approach to $C^{1, α}$ estimates for weak solutions of quasilinear parabolic equations, the prototype example being

u_{t} - div (∣\nabla u ∣^{p - 2} \nabla u) = 0.

without having to consider the singular and degenerate cases separately. This is achieved via a new scaling and a suitable adaptation of the covering argument developed by E. DiBenedetto and A. Friedman.

Cite this article

Adimurthi, Agnid Banerjee, Unified approach to $C^{1, α}$ regularity for quasilinear parabolic equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 4, pp. 833–883

DOI 10.4171/RLM/990