A priori conditions for linear second order elliptic equations in two variables in unbounded domains
The author considers a homogeneous Dirichlet problem in an unbounded plane domain A related to a second-order uniformly elliptic linear operator L. The coefficients of L are assumed to be measurable and bounded and to admit limits as x tends to infinity. Taking advantage of a basic result by \textit{G. Talenti} [Matematiche 21, 339-376 (1966; Zbl 0149.074)], and introducing suitable classes of domains and weights g, the author proves, via some apriori estimates, that the operator L, restricted to the Sobolev weighted space \(W^ 2_ 0(A,g(x)dx),\) has a finite dimensional kernel and a closed range.
scientific article; zbMATH DE number 3877614