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Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 23 Jan 2014Embargo end date: 01 Jan 2012 English Publisher:Springer Science and Business Media LLCJournal:Archive for Rational Mechanics and Analysis, volume 212, pages 129-177 (issn: 0003-9527, eissn: 1432-0673, Copyright policy )
Authors: Andrea Cianchi; Vladimir Maz'ya; Vladimir Maz'ya;

doi: 10.1007/s00205-013-0705-x , 10.48550/arxiv.1212.5773

arXiv: http://arxiv.org/abs/1212.5773

handle: 2158/841499

Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems

Abstract

Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed. The case of arbitrary bounded convex domains is also included.

Related Organizations
Keywords

Mathematics - Analysis of PDEs, Nonlinear elliptic systems; Dirichlet problem; Neumann problem; Global boundedness of the gradient; Lipschitz regularity; Lorentz spaces, FOS: Mathematics, 35B45, 35J25, Analysis of PDEs (math.AP)

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    		 116
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    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
116
Top 1%
Top 10%
Top 10%
Green
bronze