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: -Delta(p)u = sigma u(q) + mu, F-k vertical bar-u vertical bar = sigma u(q) + mu, u >= 0, on R-n, or on a bounded domain Omega subset of R-n. Here Delta(p) is the p-Laplacian defined by Delta(p)u = div(del u vertical bar del u vertical bar(p-2)), and F-k vertical bar u vertical bar is the k-Hessian, i.e., the sum of the k x k principal minors of the Hessian matrix D(2)u (k = 1, 2, ... , n); sigma and mu are general nonnegative measurable functions (or measures) on Omega. (C) 2009 Elsevier Inc. All rights reserved.