The Cauchy problem for Douglis-Nirenberg elliptic systems of partial differential equations
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- by Richard J. Kramer PDF
- Trans. Amer. Math. Soc. 182 (1973), 211-225 Request permission
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
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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