Hostname: page-component-7dd5485656-npwhs Total loading time: 0 Render date: 2025-10-29T06:55:42.514Z Has data issue: false hasContentIssue false
  • English
  • Français

A Quasi-Linear Elliptic Boundary Value Problem

Published online by Cambridge University Press:  20 November 2018

R. A. Adams
R. A. Adams*
Affiliation:
The University of Toronto
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 Ω be a bounded open set in Euclidean n-space, En. Let α = (α1, … , an) be an n-tuple of non-negative integers;

and denote by Qm the set ﹛α| 0 ⩽ |α| ⩽ m}. Denote by x = (x1, … , xn) a typical point in En and put

In this paper we establish, under certain circumstances, the existence of weak and classical solutions of the quasi-linear Dirichlet problem

1

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1105 - 1112
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Adams, R. A., A quasi-linear elliptic boundary value problem, Ph.D. Thesis, Univ. of Toronto, 1966.Google Scholar
2. Agmon, S., Lectures on elliptic boundary value problems (New York, 1965).Google Scholar
3. Agmon, S., The Lp-approach to the Dirichlet Problem, Ann. Scuola Norm. Sup. Pisa, 13(1959). 405–448.Google Scholar
4. Browder, F. E., On the spectral theory of elliptic differential operators I, Math. Ann., 142 (1961), 22–130.Google Scholar
5. Browder, F. E., Regularity of solutions of elliptic equations, Comm. Pure Appl. Math., 9 (1956), 351–361.Google Scholar
6. Cronin, J., Fixed points and topological degree in nonlinear analysis, A.M.S. Math. Survey No. 11 (1964).Google Scholar
7. Duff, G. F. D., Modified boundary problems for a quasi-linear elliptic equation, Can. J. Math., 8 (1956), 203–219.Google Scholar
8. Lions, J. L., Problèmes aux limites dans les équations aux dérivées partielles, Lecture Notes (Univ. of Montreal Press, 1962).Google Scholar
9. Nirenberg, L., Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math, 8 (1955), 649–672.Google Scholar
10. Vainberg, M. M., On the continuity of some operators fo a special form, Dokl. Akad. Nauk, 73 (1950), 253–255.Google Scholar