Strong Unique Continuation Property of TwO-dimensional Dirac Equations and Schrodinger Equations with Aharonov-Bohm Fields

It is well known that, if any harmonic function $u(x) $ in a domain $\Omega\subset \mathrm{R}^{n} $ satisfies $\partial_{x}^{\alpha}u(x_{0})=0$ for all multi-indices $\alpha $ at a point $x_{\mathrm{O}}\in\Omega $ , then $u(x) $ vanishes identically in $\Omega $. Recently, it is shown by Grammatico [3] that, if $\Omega $ contains the origin and $u\in W_{10\acute{\mathrm{c}}}^{22}(\Omega) $ (Sobolev space