Theoretical study demonstrates existence of bounded weak solutions in quasilinear X-elliptic equations, highlighting regularizing effects under the Q-condition.
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].
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Paolo Malanchini (2026) studied this question.
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