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The Cauchy problem for Douglis-Nirenberg elliptic systems of partial differential equations


Author: Richard J. Kramer
Journal: Trans. Amer. Math. Soc. 182 (1973), 211-225
MSC: Primary 35J55
DOI: https://doi.org/10.1090/S0002-9947-1973-0333439-1
MathSciNet review: 0333439
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Abstract: Several partial answers are given to the question: Suppose U is a solution of the Douglis-Nirenberg elliptic system $ LU = F$ where F is analytic and L has analytic coefficients. If $ U = 0$ in some appropriate sense on a hyperplane (or any analytic hypersurface) must U vanish identically?

One answer follows from introducing a so-called formal Cauchy problem for Douglis-Nirenberg 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 Douglis-Nirenberg 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 Cauchy-Kowalewski theorem applies.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0333439-1
Keywords: Cauchy problem, formal Cauchy data, Douglis-Nirenberg elliptic systems, Cauchy-Kowalewski theorem
Article copyright: © Copyright 1973 American Mathematical Society

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