Notes on Neumann Problem for Schrdinger Operators in Weighted Lipschitz Domains
Songyan Zhang · Journal of Ningbo University · 2009
Let Ω be a bounded Lipschitz domain in R n,n ≥3.Let ωα(Q)=| Q-Q0 |α,where Q0 is a fixed point on Ω.For Schrdinger equation -Δu + Vu= 0 in Ω,with singular non-negative potentials V belonging to the reverse Hlder class B∞,we study the Neumann problem with boundary data in the weighted space L2(Ω,ωα dσ),where dσ denotes the surface measure on Ω.We show that a unique solution u can be found for the Neumann problem provided 0 α n-1.Also proven is that the non-tangential maximal function of ▽u exists in L2(Ω,ωα dσ).