Global Lorentz and Lorentz–Morrey estimates below the natural exponent for quasilinear equations

Lorentz and Lorentz–Morrey estimates are obtained for gradients of very weak solutions to quasilinear equations of the form div A ( x , ∇ u ) = div | f | p - 2 f , where div A ( x , ∇ u ) is modelled after the p -Laplacian, p > 1 . The estimates are global over bounded domains that satisfy a mild...

Full description

Saved in:
Bibliographic Details
Published in:Calculus of variations and partial differential equations 2015-11, Vol.54 (3), p.3107-3139
Main Authors: Adimurthi, Karthik, Phuc, Nguyen Cong
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Lorentz and Lorentz–Morrey estimates are obtained for gradients of very weak solutions to quasilinear equations of the form div A ( x , ∇ u ) = div | f | p - 2 f , where div 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 L p energy. A higher integrability result at the boundary of the ground domain is also obtained for infinite energy solutions to the associated homogeneous equations.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-015-0895-1