Regularity for a class of strongly degenerate quasilinear operators (Q2637789)

The authors consider an operator generated by a system of Grushin vector fields. They assume that the degeneracy of the operator is in the strong \(A_\infty\) sense (the coefficients belong to a suitable Stummel-Kato type class). Moreover the assumptions on the lower order terms are minimal. In such a setting, they prove a Harnack inequality and therefore the continuity of the solutions. We remark that this paper is a step in the authors' ambitious project to study in a systematic way the smoothness properties of generalized solutions of elliptic partial differential equations.