Uniqueness of the cauchy problem for elliptic operators with fourfold characteristics of constant multiplicity
- Kyoto Univ. (Japan)
We are concerned with the uniqueness of the Cauchy problem for elliptic differential operators. This topic has a long history. In 1939, T. Carleman obtained the uniqueness result for the first order systems with simple characteristics in two independent variables. A. P. Calderon extended this result to any dimensional case by using the calculus of singular integral operators. For multiple characteristic cases, S. Mizohata proved the uniqueness for the Cauchy problem for elliptic operators with double characteristics of constant multiplicity. Later, A. P. Calderon unified these results for operators with characteristics of constant multiplicity, which are at most double while the real ones are at most simple. K.Watanabe has shown that the uniqueness for elliptic operators holds if they have at most triple characteristics of constant multiplicity. As for negative results, in 1961, A. Plis gave the nonuniqueness result for an elliptic operator having sixfold characteristics of constant multiplicity. In his article, he constructed two C{sup {infinity}} functions {alpha}(x, t) and u(x, t) defined in a neighborhood of the origin in R{sup 2} such that and suppu {contained_in} (t {ge} 0), and 0 {element_of} suppu. 25 refs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 535400
- Journal Information:
- Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 1-2 Vol. 22; ISSN 0360-5302; ISSN CPDIDZ
- Country of Publication:
- United States
- Language:
- English
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