For a concrete example, $$ \dfrac{1}{\sqrt{x_1^2 + x_2^2 + x_3^2}} - \dfrac{1}{\sqrt{(1+x_1)^2 + x_2^2 + x_3^2}}$$
is harmonic and $L^2$ on $a < x_1 < b$ if $a > 0$.