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On the behaviour near the boundary of solutions of a semi-linear partial differential equation of elliptic type

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

J. Chabrowski  and
B. Thompson
J. Chabrowski
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Qld. 4067, Australia
B. Thompson
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Qld. 4067, Australia
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The purpose of this note is to investigate traces of the functions In(1 +|u|), where u is a solution of a semi-linear partial differential equation of elliptic type, belonging to an appropriate Sobolev space. This article complements the results of Chabrowski and Thompson (1980), and Mihailov (1972), (1976).

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 4 , December 1981 , pp. 405 - 414
Copyright
Copyright © Australian Mathematical Society 1981

References

Chabrowski, J. and Thompson, B. (1980), ‘On traces of solutions of a semilinear partial differential equation of elliptic type’, Ann. Polon. Math., to appear.Google Scholar
Gilbarg, D. and Trudinger, N. S. (1977), Elliptic partial differential equation of second order (Springer-Verlag, Berlin-Heidelberg-New York).CrossRefGoogle Scholar
Kufner, A., John, D. and Fucik, S. (1977), Function spaces (Noordhoof International Publishing Leyden and Academia Publishing House of the Czechoslovak Academy of Sciences, Prague).Google Scholar
Mihailov, W. F. (1972), ‘Boundary values of solutions of elliptic equations in the ball’, Mat. Sb. 100 (142), 1–13.Google Scholar
Mihailov, W. F. (1976), ‘Boundary values of solutions of elliptic equations in a domain with smooth boundary’, Mat. Sb. 101 (143), 163–188.Google Scholar