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The Cauchy problem for Douglis-Nirenberg elliptic systems of partial differential equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kramer, Richard J. |
| Copyright Year | 1973 |
| Abstract | Several partial answers are given to the question: Suppose U is a solution of the Douglis-Nirenberg elliptic system L U = 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. |
| Starting Page | 211 |
| Ending Page | 225 |
| Page Count | 15 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9947-1973-0333439-1 |
| Volume Number | 182 |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1973-182-00/S0002-9947-1973-0333439-1/S0002-9947-1973-0333439-1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9947-1973-0333439-1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
