Gradient estimates for singular parabolic p-Laplace type equations with measure data

2021/11/04 by Dong, Hongjie, Zhu, Hanye
#31C45 #35B65 #35K67 #35K92 #35R06 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.03050

Abstract

We are concerned with gradient estimates for solutions to a class of singular quasilinear parabolic equations with measure data, whose prototype is given by the parabolic p-Laplace equation u_t-Δ_p u=μ with p∈ (1,2). The case when p∈ (2-(1)/(n+1),2) were studied in [15]. In this paper, we extend the results in [15] to the open case when p∈ ((2n)/(n+1),2-(1)/(n+1)] if n≥ 2 and p∈((5)/(4), (3)/(2)] if n=1. More specifically, in a more singular range of p as above, we establish pointwise gradient estimates via linear parabolic Riesz potential and gradient continuity results via certain assumptions on parabolic Riesz potential.

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