(untitled) (Journal of Partial Differential Equations, 1995)
This paper proves the existence of solution for the following quasilinear subelliptic Dirichlet problem: Σ^m_j=1X^∗_ja_j(X, v, Xv)+ a_o(x, v, Xv) + H(x,v, Xv) = 0 v ∈ M^1,p_0(Ω) ∩ L^∞(Ω) Here X = X_1 , …, X_m is a system of vector fields defined in an open domain M of R^n, n ≥ 2, Ω ⊂ ⊂ M, and X satisfies the so-called Hormander's condition at the order of r > 1 on M. M_1,p_0(Ω) is the weighted Sobolev's space associated with the system X . The Hamiltonian H grows at most like |Xv|^p.