Tohoku Mathematical Journal

Strong unique continuation property for elliptic systems of normal type in two independent variables

Takashi Ōkaji

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Abstract

We give a result on strong unique continuation property for a certain elliptic system of first order in the two dimensional space. Two coefficient matrices are normal and commutative with each other. We assume, further, that their components are Hölder continuous and have continuous first order derivatives except at one point. Without any regularity assumptions on the eigenvalues, we can show the strong unique continuation property for a class of such systems under certain quantitative conditions on the first order derivatives. This result gives an improvement of a work by G. N. Hile and M. H. Protter in a special case.

Article information

Source
Tohoku Math. J. (2), Volume 54, Number 2 (2002), 309-318.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113247569

Digital Object Identifier
doi:10.2748/tmj/1113247569

Mathematical Reviews number (MathSciNet)
MR1904955

Zentralblatt MATH identifier
1016.35010

Subjects
Primary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]
Secondary: 35J45

Citation

Ōkaji, Takashi. Strong unique continuation property for elliptic systems of normal type in two independent variables. Tohoku Math. J. (2) 54 (2002), no. 2, 309--318. doi:10.2748/tmj/1113247569. https://projecteuclid.org/euclid.tmj/1113247569


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References

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