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

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