Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-22T00:27:46.986Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Local Elliptic Boundary-Value Problems

Published online by Cambridge University Press:  20 November 2018

Bui An Ton
Bui An Ton*
Affiliation:
Université de Montréal, Montréal, P.Q.; University of British Columbia, Vancouver, B.C.
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.

Let G be a bounded open set of Rn with a smooth boundary ∂G. We consider the following elliptic boundary-value problem:

where A and Bj are, respectively singular integro-differential operators on G and on ∂G, of orders 2m and rj with rj < 2m; Ck are boundary differential operators, and Ljk are linear operators, bounded in a sense to be specified.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1365 - 1382
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Agmon, S., On the eigenfunctions and on the eigenvalues of general elliptic boundary-value problems, Comm. Pure Appl. Math. 15 (1962), 119–147.Google Scholar
2. Agranovic, M. S., Elliptic singular integro-differential operators, Uspehi Mat. Nauk 20 1965), no. 5, 3-120 = Russian Math. Surveys 20 (1965), no. 5-6, 2–116.Google Scholar
3. Agranovic, M. S. and Visik, M. I., Elliptic problems with a parameter and parabolic problems of general type, Uspehi Mat. Nauk 19 (1964), no. 3, 53-161 = Russian Math. Surveys 19 (1964), no. 3, 53–157.Google Scholar
4. Beals, R., Nonlocal boundary-value problems for elliptic operators, Amer. J. Math. 57(1965), 315–362.Google Scholar
5. Browder, F. E., A-priori estimates for solutions of elliptic boundary-value problems. I, II, Nederl. Akad. Wetensch. Proc. Ser. A 63 = Indag. Math. 22 (1960), 145-149,160-169; III, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 404–410.Google Scholar
6. Browder, F. E., Nonlocal elliptic boundary-value problems, Amer. J. Math. 86 (1964), 735–750.Google Scholar
7. Browder, F. E., Problèmes non-linéaires, Séminaires Math. Sup. (Univ. Montreal Press, Montreal, 1965).Google Scholar
8. Schechter, M., Nonlocal elliptic boundary-value problems, Ann. Scuola Norm. Sup. Pisa (3) 20 (1966), 421–441.Google Scholar
9. Sobolevskiĭ, P. E., Equations of parabolic type in a Banach space, Trudy Moskov. Mat. Obšč. 10 (1961), 297-350 = Amer. Math. Soc. Transi. (2) (49), 1–62.Google Scholar
10. Ton, B. A., On nonlinear elliptic boundary-value problems, Bull. Amer. Math. Soc. 72 1966), 307–313.Google Scholar