= Solution
For a time-independent field, <Faraday's law> gives $\nabla\times\mathbf E=0$. Integrating around a thin rectangular loop crossing $x=0$ and shrinking its height gives continuity of the <tangential component>:
$$
\boxed{E_y^-=E_y^+,qquad E_z^-=E_z^+}.
$$
A thin <Gaussian pillbox> and $\nabla\cdot\mathbf D=0$ give continuity of the normal <electric displacement field>:
$$
\boxed{D_x^-=D_x^+,qquad \varepsilon_-E_x^-=\varepsilon_+E_x^+}.
$$
These are the electrostatic cases of the <dielectric-interface boundary conditions>.
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