Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity q > 1 and with natural growth

In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q  > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem a...

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Bibliographic Details
Published in:Journal of global optimization 2008-03, Vol.40 (1-3), p.99-117
Main Authors: Giuffrè, Sofia, Idone, Giovanna
Format: Article
Language:English
Subjects:
Computer Science
Dirichlet problem
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Optimization
Partial differential equations
Real Functions
Studies
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Summary:In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second-order discontinuous elliptic systems with nonlinearity q  > 1 and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension n  =  q without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets , are always empty for n  =  q . Moreover we show that also for 1 
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-007-9174-9