(untitled) (Journal of Partial Differential Equations, 1998)
We are concerned with the Dirichlet problem of div A(x, Du) + B(z) = 0 in Ω u= u_0 on ∂ Ω Here Ω ⊂ R^N is a bounded domain, A(x, p) = (A¹ (x, p), ... >A^N (x, p) satisfies min|p|^1+α, |p|^1+β ≤ A(x, p) ⋅ p ≤ α_0(|p|^1+α+|p|^1+β) with 0 < α ≤ β. We show that if A is Lipschitz, B and u_0 are bounded and β < max N+2Nα + 2N,α + 2, then there exists a C¹-weak solution of (0.1).