W^1,p estimates for Schrödinger equation in the region above a convex graph

2024/11/28 by Xu, Ziyi
#35B45 #35J10 #35J25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.18852

Abstract

We investigate the W^1,p estimates of the Neumann problem for the Schrödinger equation -Δu+ V u=\rm div(f) in the region above a convex graph. For any p>2, we obtain a sufficient condition for the W^1,p solvability. As a result, we obtain sharp W^1,p estimate ‖∇ u‖_L^p(Ω)+‖V^(1)/(2)u‖_L^p(Ω)≤ C‖f‖_L^p(Ω) for 1

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