Regularizing effect in quasilinear X-elliptic equations with natural growth term

Abstract In this paper, we investigate the regularizing effect arising from the interplay between coefficients in quasilinear problems involving X -elliptic operators, a class of degenerate operators introduced by Lanconelli and Kogoj in [15]. Due to the presence of a natural growth term, the problem lacks a variational structure. By combining a suitable approximation scheme with Schauder’s fixed point theorem, we prove the existence of bounded weak solutions if the coefficients satisfy the Q -condition introduced by Arcoya and Boccardo in [1].