Tohoku Mathematical Journal
2002
June
SECOND SERIES VOL. 54, NO. 2

Tohoku Math. J.
54 (2002), 309-318

Title STRONG UNIQUE CONTINUATION PROPERTY FOR ELLIPTIC SYSTEMS OF NORMAL TYPE IN TWO INDEPENDENT VARIABLES

Dedicated to Professor Norio Shimakura on his sixtieth birthday
Author Takashi Ōkaji

(Received June 28, 2000, revised April 9, 2001)
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 Holder 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.

2000 Mathematics Subject Classification. Primary 35B05; Secondary 35J45.
Key words and phrases. Strong unique continuation, Elliptic system.

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