Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-15T17:42:20.733Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates for General Coercive Boundary Problems on a Half-Space for a Class of Elliptic Partial Differential Operators

Published online by Cambridge University Press:  20 November 2018

Peter C. Greiner
Peter C. Greiner*
Affiliation:
University of Toronto, Toronto, Ontario
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.

In recent years elliptic boundary value problems have been studied in great detail; see, for example, Agmon (1), Agmon, Douglis, and Nirenberg (2), Browder (4), Hormander (7), Schechter (10; 11; 12), Agranovich and Dynin (3). In all these cases the boundary problems considered were local or semilocal, i.e. the boundary operators involved are differential operators possibly having singular integral operators for coefficients (cf. (3)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 679 - 697
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

A portion of the research contained in this paper was completed by the author while he held a Fellowship at the Summer Research Institute of the Canadian Mathematical Congress organized at Queen's University during the summer of 1966.

References

1. Agmon, S., The coerciveness problem for integro-differential forms, J. Analyse Math., 6 1958), 183–223.Google Scholar
2. Agmon, S., Douglis, A., and Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623–727.Google Scholar
3. Agranovich, M. S. and Dynin, A. S., General boundary-value problems for elliptic systems in an n-dimensional domain, Dokl. Akad. Nauk SSSR, 146 (1962), 511-514 (Soviet Math. Dokl., Vol. 3, no. 5, 1323–1327).Google Scholar
4. Browder, F., A priori estimates for solutions of elliptic boundary-value problems. I, II, III, Nederl. Akad. Wetensch. Proc. Ser. A, 22 (1960), 145-159, 160-169; 23 (1961), 404–410.Google Scholar
5. Browder, F., On the spectral theory of elliptic differential operators, Math. Ann., 142 (1961), 22–130.Google Scholar
6. Browder, F., Non-local elliptic boundary value problems, Amer. J. Math., 86 (1964), 735–750.Google Scholar
7. Hörmander, L., On the regularity of the solutions of boundary problems, Acta. Math., 99 1958), 225–264.Google Scholar
8. Hörmander, L., Linear partial differential operators (Springer, Berlin, 1963).10.1007/978-3-642-46175-0CrossRefGoogle Scholar
9. Peetre, J., On estimating the solutions of hypo-elliptic differential equations near the plane boundary, Math. Scand., 9 (1961), 337–351.Google Scholar
10. Schechter, M., On estimating elliptic partial differential operators in the L2 norm, Amer. J. Math., 79 (1957), 431–443.Google Scholar
11. Schechter, M., Integral inequalities for partial differential operators and functions satisfying general boundary conditions, Comm. Pure Appl. Math., 12 (1959), 37–66.Google Scholar
12. Schechter, M., On the dominance of partial differential operators. II, Ann. Scuola Norm. Sup. Pisa, Ser. 3, 18 (1964), 255–282.Google Scholar
13. Schechter, M., Remarks on elliptic boundary value problems, Comm. Pure Appl. Math., 12 (1959), 561–578.Google Scholar
14. Titchmarsh, E. C., Introduction to the theory of Fourier integrals (Clarendon Press, Oxford, 1959).Google Scholar
15. Višik, M. I., On general boundary-value problems for elliptic partial differential equations, Trudy Moskov. Mat. Obsc., / (1952), 187-246 (AMS Transi. (2), 24 (1963), 107–172).Google Scholar