Mixed Boundary Value Problem for the Helmholtz Equation in a Model 2D Double Angular Domain

The purpose of the present research is to investigate mixed boundary value problem for the Helmholtz equation in a model 2D double angular domains $$\Omega _{\alpha ,\beta }:=\Omega _\alpha \cup \Omega _{-\beta }\subset \mathbb {R}^2$$ , where $$\Omega _\alpha $$ has magnitude $$\alpha >0$$ and $$\Omega _{-\beta }\subset \mathbb {R}^2$$ has magnitude $$-\beta >0$$ . Angular domain $$\Omega _\alpha $$ and $$\Omega _{-\beta }$$ have common boundary along the positive semi-axes $$\mathbb {R}^+:=(0,\infty )$$ . The BVP is considered in a nonclassical setting, when solutions are sought in the Bessel potential spaces $$\mathbb {H}^s_p(\Omega _{\alpha ,\beta })$$ , $$s>1/p$$ , $$1