On the problem of unique continuation for the p-Laplace equation

We study if two different solutions of the p-Laplace equation ∇⋅(|∇u|p−2∇u)=0, where 1<p<∞, can coincide in an open subset of their common domain of definition. We obtain some partial results on this interesting problem.

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Bibliographic Details
Published inNonlinear analysis Vol. 101; pp. 89 - 97
Main Authors Granlund, Seppo, Marola, Niko
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2014
Subjects
[formula omitted]-harmonic function
Frequency function
Infinity
Mathematical analysis
Nonlinearity
Triangles
secondary
Frequency function
primary
p-harmonic function
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Summary:We study if two different solutions of the p-Laplace equation ∇⋅(|∇u|p−2∇u)=0, where 1<p<∞, can coincide in an open subset of their common domain of definition. We obtain some partial results on this interesting problem.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2014.01.020