  The purpose of the present research is to investigate model mixed boundary
value problems for the Helmholtz equation in a planar angular domain
$\Omega_\alpha\subset\mathbb{R}^2$ of magnitude $\alpha$. The BVP is considered
in a non-classical setting when a solution is sought in the Bessel potential
spaces $\mathbb{H}^s_p(\Omega_\alpha)$, $s>1/p$, $1<p<\infty$. The problems are
investigated using the potential method by reducing them to an equivalent
boun\-dary integral equation (BIE) in the Sobolev-Slobode\v{c}kii space on a
semi-infinite axes $\bW^{s-1/p}_p(\bR^+)$, which is of Mellin convolution type.
By applying the recent results on Mellin convolution equations in the Bessel
potential spaces obtained by V. Didenko \& R. Duduchava in \cite{DD16},
explicit conditions of the unique solvability of this BIE in the
Sobolev-Slobode\v{c}kii $\bW^r_p(\bR^+)$ and Bessel potential
$\bH^r_p(\mathbb{R}^+)$ spaces for arbitrary $r$ are found and used to write
explicit conditions for the Fredhoilm property and unique solvability of the
initial model BVPs for the Helmholtz equation in the above mentioned
non-classical setting.
  The same problem was investigated in the foregoing paper of the authors
published in 2013, but there was made fatal errors. In the present paper we
correct these results.
