Interaction of boundary singular points in an elliptic boundary value problem

The paper continues the construction of the $L_p$-theory of elliptic Dirichlet and Neumann boundary value problems with discontinuous piecewise constant coefficients in divergent form for an unbounded domain $\Omega\subset\mathbb{R}^2$ with a piecewise $C^1$ smooth noncompact Lipschitz boundary and $C^1$ smooth discontinuity lines of the coefficients. An earlier constructed $L_p$-theory is generalized to the case of different smallest eigenvalues corresponding to a finite and an infinite singular point, and the effect of their interaction is further studied in the class of functions with first derivatives from $L_p(\Omega)$ in the entire range of the exponent $p\in(1,\infty)$.