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# On the Neumann Problem for the Schrödinger Equations with Singular Potentials in Lipschitz Domains

Published:2004-06-01
Printed: Jun 2004
• Xiangxing Tao
• Henggeng Wang
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## Abstract

We consider the Neumann problem for the Schr\"odinger equations $-\Delta u+Vu=0$, with singular nonnegative potentials $V$ belonging to the reverse H\"older class $\B_n$, in a connected Lipschitz domain $\Omega\subset\mathbf{R}^n$. Given boundary data $g$ in $H^p$ or $L^p$ for $1-\epsilon  Keywords: Neumann problem, Schrödinger equation, Lipschitz, domain, reverse Hölder class,$H^p\$ space
 MSC Classifications: 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 35J10 - Schrodinger operator [See also 35Pxx]