Regularity results for a noncoercive nonlinear Dirichlet problem

Abstract

In this paper, we prove some regularity results for a noncoercive nonlinear Dirichlet problem in an unbounded domain. The main result is obtained in the hypothesis that suitable coefficients of the operator associated to the problem belong to a class of functional spaces strictly containing Lebesgue ones. This can be done by approximation via coercive nonlinear Dirichlet problems. Under additional assumptions, we also get the boundedness of a solution.