Pointwise A Priori Estimates for Solutions to Some p-Laplacian Equations

2021/07/27 by Sun, Xiaoqiang, Bao, Jiguang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.12767

Abstract

In this paper, we apply blow-up analysis and Liouville type theorems to study pointwise a priori estimates for some quasilinear equations with p-Laplace operator. We first obtain pointwise interior estimates for the gradient of p-harmonic function, i.e., the solution of Δ_pu=0, x∈Ω, which extends the well-established results of the interior estimates of the gradient of harmonic function. We then get singularity and decay estimates of the sign changing solution of Lane-Emden-Fowler type p-Laplace equation -Δ_pu=|u|^λ-1u, x∈Ω, which are then generalized for the equation with general right hand term f(x,u), under some asymptotic conditions of f. Lastly, we get pointwise estimates for higher order derivatives of the solution of -Δu=u^λ,x∈Ω, the case of p=2 for p-Laplace equation.

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