Document Type
Article
Publication Date
3-15-2016
Abstract
In the framework of Morrey or Lorentz-Morrey spaces, we characterize the existence of solutions to the quasilinear Riccati type equation. with a distributional datum σ. Here div A(x, ∇u) is a quasilinear elliptic operator modelled after the p-Laplacian, p >. 1, but with a very general nonlinear structure, and Ω is a sufficiently flat domain in the sense of Reifenberg. The existence results are obtained in the natural or super-natural range of the gradient growth, i.e., q≥. p.Motivated by the analysis of quasilinear Riccati type equation, a substantial part of the paper is also devoted to the Calderón-Zygmund type gradient regularity for the boundary value problem. We obtain regularity estimates in some weighted and unweighted function spaces as well as natural Lorentz-Morrey spaces associated to the Riccati type equation above.
Publication Source (Journal or Book title)
Journal of Differential Equations
First Page
5421
Last Page
5449
Recommended Citation
Mengesha, T., & Phuc, N. (2016). Quasilinear Riccati type equations with distributional data in Morrey space framework. Journal of Differential Equations, 260 (6), 5421-5449. https://doi.org/10.1016/j.jde.2015.12.007