Existence, Regularity, and Uniqueness of Solutions to Some Noncoercive Nonlinear Elliptic Equations in Unbounded Domains.

In this paper, we study a noncoercive nonlinear elliptic operator with a drift term in an unbounded domain. The singular first-order term grows like | E (x) | | ∇ u | , where E (x) is a vector field belonging to a suitable Morrey-type space. Our operator arises as a stationary equation of diffusion–advection problems. We prove existence, regularity, and uniqueness theorems for a Dirichlet problem. To obtain our main results, we use the weak maximum principle and the same a priori estimates. [ABSTRACT FROM AUTHOR]