Abstract:
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 $p\in(1,\infty)$.
Key words:elliptic equation in divergent form, discontinuous piecewise constant coefficient, unbounded domain, piecewise smooth noncompact Lipschitz boundary, smooth discontinuity lines of coefficient, Dirichlet problem, Neumann problem, weak solution with first derivatives from $L_p$, $L_p$-theory, interaction of singularities.
