Entropy solutions of the Zaremba (Neumann) problem in an unbounded domain for an elliptic equation with measure-valued potential.

he existence of entropy solutions to the Zaremba or Neumann problems in an unbounded domain is established for the equation of the form $A(u)+b_0(x,u,\nabla u)+b_1(x,u)\mu=f$ with bounded Radon measure $\mu$. On the growth of functions $b_0, b_1$ with respect to the variable $u$ no restrictions are imposed, but its increase is assumed. Under some additional restrictions, the uniqueness of the entropy solution to the external Zaremba (Neumann) problem is established.