Singular quasilinear and Hessian equations and inequalities

We solve the existence problem in the renormalized, or viscosity sense, and obtain global pointwise estimates of solutions for quasilinear and Hessian equations with measure coefficients and data, including the following model problems: − pu = σuq +μ, Fk [−u] = σuq +μ, u 0, on Rn, or on a bounded domain Ω ⊂ Rn. Here p is the p-Laplacian defined by pu = div(∇u|∇u|p−2), and Fk [u] is the k-Hessian, i.e., the sum of the k × k principal minors of the Hessian matrix D2u (k = 1, 2, . . . , n); σ and μ are general nonnegative measurable functions (or measures) on Ω. © 2009 Elsevier Inc. All rights reserved.