Summary: We consider a bulk charge potential of the form \[ u(x) = \int\limits_\Omega {g(y)F(x - y)dy,\qquad x = ({x_1},{x_2},{x_3}) \in {\mathbb{R}^3},} \] where \({\Omega}\) is a layer of small thickness \(h > 0\) located around the midsurface \({\Sigma}\), which can be either closed or open, and \(F(x-y)\) is a function with a singularity of the form \(1/|x-y|\). We prove that, under certain assumptions on the shape of the surface \({\Sigma}\), the kernel \(F\), and the function \(g\) at each point \(x\) lying on the midsurface \({\Sigma}\) (but not on its boundary), the second derivatives of the function \(u\) can be represented as \[ \frac{{{\partial ^2}u(x)}}{{\partial {x_i}\partial {x_j}}} = h\int\limits_\Sigma {g(y)\frac{{{\partial ^2}F(x - y)}}{{\partial {x_i}\partial {x_j}}}} dy - {n_i}(x){n_j}(x)g(x) + {\gamma _{ij}}(x),\qquad i,j = 1,2,3, \] where the function \(\gamma_{ij}(x)\) does not exceed in absolute value a certain quantity of the order of \(h^2\), the surface integral is understood in the sense of Hadamard finite value, and the \(n_i(x)\), \(i = 1, 2, 3\), are the coordinates of the normal vector on the surface \({\Sigma}\) at a point \(x\).