onto the eigenmodes of color charged fields on the sharp wall can be obtained from the requirement of preservation of the properties of eigenmodes for finite $\mu$ as far as they can be identified. The continuity of the normal to the wall component of the total (through the whole hypersurface of the wall) charged current offers a reliable guiding principle for identification of the matching conditions. Continuity of the total current means that the surface terms do not appear under integration by parts in the action, $$\begin{aligned}
\label{current_cont_sc}
&&\lim_{\varepsilon\to 0}\left[J_1(\varepsilon)-J_1(-\varepsilon)\right]=0,
\\
\nonumber
&&J_\mu(x_1)=\int d^3x \Phi^\dagger(x)D_\mu\Phi(x),
\\
\nonumber
&&d^3x=dx_2dx_3dx_4.\end{aligned}$$ Moreover, this requirement restricts the form of the eigenfunctions in such a way that the surface terms associated with the gauge dependent delta-function singularuties in $\partial_\mu \breve B_\mu$, Eq.(\[sing\_gauge\]) vanish as well.

![Derivatives of the components of the chromomagnetic field are plotted for two values of the width parameter $\mu/\sqrt{B}=3,10$.The coordinate $x_1$ is given in units of $1/\sqrt{B}$. In the limit of the infinitely thin domain wall ($\mu/\sqrt{B}\to\infty$) the derivatives develop the delta-function singularities at the location of the wall. []{data-label="Fig:der_single_kink"}](derivH.eps){width="75mm"}

Confined fluctuations in the bulk
---------------------------------

Let us consider the eigenvalue problem $$\begin{aligned}
\label{scalar1}
&&-\tilde D^2\Phi=\lambda\Phi.\end{aligned}$$ for the functions square integrable 