Foundations of the nonlinear theory of the potential of elliptic equations (Q1593946)

The paper deals with the boundary behaviour of solutions and supersolutions of the equation \[ -\text{div } A(x,\nabla_{L}u)=0, \] where \(\nabla_L u=(X_1u,\ldots,X_ku)\) is the subgradient defined by the \(C^\infty\)-vector fields \((X_1,\ldots,X_k)\) satisfying Hörmander's hypoellipticity condition and the mapping \(A\colon\;\Omega\times {\mathbb R}^k\to {\mathbb R}^k\) satisfies some natural growth conditions. The authors establish very interesting qualitative results (comparison and maximum principles, regularity results, Wiener test) in weighted Sobolev spaces for solutions of the above equation.