Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T00:01:30.221Z Has data issue: false hasContentIssue false

On the Uniqueness in Cauchy’s Problem for Elliptic Systems with Double Characteristics

Published online by Cambridge University Press:  22 January 2016

Kazunari Hayashida*
Affiliation:
Mathematical Institute, Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider in the 2 dimensional space with the coordinate (x,y). Let Γ be a segment of the y-axis containing the origin in its interior and let Ω be a domain whose boundary contains Γ.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Calderón, A.P., Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math., 80 (1958), 1636.Google Scholar
[2] Carleman, T., Sur un problème d’unicité pour les systems d’équations aux dérivées partielles a deux variables independents, Arkiv Math., 26 B (1938), 19.Google Scholar
[3] Douglis, A., On uniqueness in Cauchy problems for elliptic systems of equations, Comm. Pure Appl. Math., 13 (1960), 593607.Google Scholar
[4] Hayashida, K., On the uniqueness in Cauchy’s problem for elliptic equations, RIMS Kyoto Univ., Ser. A, 2 (1967), 429449.Google Scholar
[5] Hörmander, L., On the uniqueness of the Cauchy problem I-II, Math. Scand., 6 (1958), 213225; 7 (1959), 177190.Google Scholar
[6] Kumano-Go, H., Unique continuation for elliptic equations, Osaka Math. J., 15 (1963), 151172.Google Scholar
[7] Landis, E.M., On some properties of elliptic equations, Dokl. Akad. Nauk SSSR, 107 (1956), 640643 (Russian).Google Scholar
[8] Lavrentév, M.M., On Cauchy’s boundary value problem for linear elliptic equations of the second order, Dokl. Adak. Nauk SSSR, 112 (1957) 195197.Google Scholar
[9] Mergelyan, S.N., Harmonic approximation and approximate solution of Cauchy’s problem for Laplace equation, Dokl. Akad. Nauk SSSR, 107 (1956), 644647 (Russian).Google Scholar
[10] Mizohata, S., Unicité du prolongement des solutions des équation elliptiques du quatrième ordre, Proc. Japan Acad., 34 (1958), 687692.Google Scholar
[11] Pederson, R.N., On the unique continuation theorem for certain second and fourth order elliptic equations, Comm. Pure Appl. Math., 9 (1958), 6780.Google Scholar
[12] Protter, M.H., Unique continuation for elliptic equations, Trans. Amer. Math. Soc, 95 (1960), 8191.Google Scholar
[13] Shirota, T., A remark on the unique continuation theorem for certain fourth order elliptic equations, Proc. Japan Acad., 36 (1960), 571573.Google Scholar