Global Lorentz and Lorentz–Morrey estimates below the natural exponent for quasilinear equations
Document Type
Article
Publication Date
11-1-2015
Abstract
Lorentz and Lorentz–Morrey estimates are obtained for gradients of very weak solutions to quasilinear equations of the form (Formula Presented.),where A(x,∇u) is modelled after the p-Laplacian, p>1. The estimates are global over bounded domains that satisfy a mild exterior uniform thickness condition that involves the p-capacity. The vector field datum f is allowed to have low degrees of integrability and thus solutions may not have finite Lp energy. A higher integrability result at the boundary of the ground domain is also obtained for infinite energy solutions to the associated homogeneous equations.
Publication Source (Journal or Book title)
Calculus of Variations and Partial Differential Equations
First Page
3107
Last Page
3139
Recommended Citation
Adimurthi, K., & Phuc, N. (2015). Global Lorentz and Lorentz–Morrey estimates below the natural exponent for quasilinear equations. Calculus of Variations and Partial Differential Equations, 54 (3), 3107-3139. https://doi.org/10.1007/s00526-015-0895-1