The Cauchy problem for DouglisNirenberg elliptic systems of partial differential equations
Author:
Richard J. Kramer
Journal:
Trans. Amer. Math. Soc. 182 (1973), 211225
MSC:
Primary 35J55
MathSciNet review:
0333439
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Abstract: Several partial answers are given to the question: Suppose U is a solution of the DouglisNirenberg elliptic system where F is analytic and L has analytic coefficients. If in some appropriate sense on a hyperplane (or any analytic hypersurface) must U vanish identically? One answer follows from introducing a socalled formal Cauchy problem for DouglisNirenberg elliptic systems and establishing existence and uniqueness theorems. A second Cauchy problem, in some sense a more natural one, is discussed for an important subclass of the DouglisNirenberg elliptic systems. The results in this case give a second partial answer to the original question. The methods of proof employed are largely algebraic. The systems are reduced to systems to which the CauchyKowalewski theorem applies.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197303334391
PII:
S 00029947(1973)03334391
Keywords:
Cauchy problem,
formal Cauchy data,
DouglisNirenberg elliptic systems,
CauchyKowalewski theorem
Article copyright:
© Copyright 1973
American Mathematical Society
