Singular quasilinear and Hessian equations and inequalities

Authors

Nguyen Cong Phuc, Louisiana State University
Igor E. Verbitsky, University of Missouri

Document Type

Article

Publication Date

3-15-2009

Abstract

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:- Δp u = σ u^q + μ, Fk [- u] = σ u^q + μ, u ≥ 0, on Rⁿ, or on a bounded domain Ω ⊂ Rⁿ. Here Δp is the p-Laplacian defined by Δp u = 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 D² u (k = 1, 2, ..., n); σ and μ are general nonnegative measurable functions (or measures) on Ω. © 2009 Elsevier Inc. All rights reserved.

Publication Source (Journal or Book title)

Journal of Functional Analysis

First Page

1875

Last Page

1906

Recommended Citation

Phuc, N., & Verbitsky, I. (2009). Singular quasilinear and Hessian equations and inequalities. Journal of Functional Analysis, 256 (6), 1875-1906. https://doi.org/10.1016/j.jfa.2009.01.012