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Borderline gradient estimates at the boundary in Carnot groups
Part of:
Elliptic equations and systems
Miscellaneous topics - Partial differential equations
Partial differential equations
Published online by Cambridge University Press: 02 December 2020
Abstract
In this article, we prove the continuity of the horizontal gradient near a C1,Dini non-characteristic portion of the boundary for solutions to 
$\Gamma ^{0,{\rm Dini}}$ perturbations of horizontal Laplaceans as in (1.1) below, where the scalar term is in scaling critical Lorentz space L(Q, 1) with Q being the homogeneous dimension of the group. This result can be thought of both as a sharpening of the 
$\Gamma ^{1,\alpha }$ boundary regularity result in [4] as well as a subelliptic analogue of the main result in [1] restricted to linear equations.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1920 - 1953
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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