On the W²_p Estimate for Oblique Derivative Problem in Lipschitz Domains

2018/08/06 by Dong, Hongjie, Li, Zongyuan
#35J25 (Primary) #35J60 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.02124

Abstract

The aim of this paper is to establish W²_p estimate for non-divergence form second-order elliptic equations with the oblique derivative boundary condition in domains with small Lipschitz constants. Our result generalizes those in [14, 15], which work for C^1,α domains with α> 1-1/p. As an application, we also obtain a solvability result. An extension to fully nonlinear elliptic equations with the oblique derivative boundary condition is also discussed.

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