Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-22T15:45:51.606Z Has data issue: false hasContentIssue false
  • English
  • Français

On the regularity of solutions to quasi-linear variational inequalities of degenerate elliptic type*

Published online by Cambridge University Press:  14 February 2012

Frances Cooper
Frances Cooper
Affiliation:
Department of Mathematics, University of Glasgow
Get access Rights & Permissions [Opens in a new window]

Synopsis

Using the theory of the weighted Sobolev space H1,2(μ), on a bounded domain Ω, in Rn, the existence and regularity of solutions u in K to the variational inequality

is established for various convex subsets K of H1, 2(μ). The growth conditions imposed on the functions A and B give the differential inequality degenerate elliptic structure, extending the results on regularity for inequalities of elliptic type.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 251 - 263
Copyright
Copyright © Royal Society of Edinburgh 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Browder, F. E.. Existence theorems for non-linear partial differential equations. Proc. Symp. Pure Math. 16 (Providence, R.I.: Amer. Math. Soc, 1970).Google Scholar
2Krasnosel'skii, M. A.. Topological methods in the theory of non-linear integral equations (London: Pergamon, 1964).Google Scholar
3Lions, J. L.. Quelques méthodes de résolution des problèmes aux limites non-linéaires (Paris: Dunod, Gauthier-Villars, 1969).Google Scholar
4Murthy, M. K.V. and Stampacchia, G.. Boundary value problems for some degenerate elliptic equations. Ann. Mat. Pura Appl. 80 (1968), 1–122.Google Scholar
5Stampacchia, G.. Régularisation des solutions de problèmes aux limites elliptiques à données discontinues. Proc. Internat. Symp. Linear Spaces Jerusalem 339–408 (Jerusalem: Academic Press and London: Pergamon, 1960).Google Scholar
6Veiga, H. B. da. Sur la régularité des solutions de l' équation div A(x, u, ∇u) = B (x, u, ∇u) avec des conditions aux limites unilaterales et melees. Ann. Mat. Pura Appl. 93 (1972), 173–230.CrossRefGoogle Scholar