Document Type
Article
Publication Date
3-1-2011
Abstract
Global weighted Lp estimates are obtained for the gradient of solutions to nonlinear elliptic Dirichlet boundary value problems over a bounded nonsmooth domain. Morrey and Hölder regularity of solutions are also established, as a consequence. These results generalize various existing estimates for nonlinear equations. The nonlinearities are of at most linear growth and assumed to have a uniform small mean oscillation. The boundary of the domain, on the other hand, may exhibit roughness but assumed to be sufficiently flat in the sense of Reifenberg. Our approach uses maximal function estimates and Vitali covering lemma, and also known regularity results of solutions to nonlinear homogeneous equations. © 2010 Elsevier Inc.
Publication Source (Journal or Book title)
Journal of Differential Equations
First Page
2485
Last Page
2507
Recommended Citation
Mengesha, T., & Phuc, N. (2011). Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains. Journal of Differential Equations, 250 (5), 2485-2507. https://doi.org/10.1016/j.jde.2010.11.009