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On the boundary values of the solutions of linear elliptic equations

Published online by Cambridge University Press:  17 April 2009

J. Chabrowski  and
H.B. Thompson
J. Chabrowski
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4067, Australia.
H.B. Thompson
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4067, Australia.
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Abstract

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The purpose of this article is to investigate the traces of weak solutions of a linear elliptic equation. In particular, we obtain a sufficient condition for a solution belonging to the Sobolev space to have an L2-trace on the boundar.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1983 , pp. 1 - 30
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Chabrowski, J. and Thompson, B., “On traces of solutions of a semi-linear partial differential equation of elliptic type”, Ann. Polon. Math, (to appear).Google Scholar
[2]Gilbarg, David and Trudinger, Neil S., Elliptic partial differential equations of second order (Die Grundlehren der mathematischen Wissenschaften), 224. Springer-Verlag, Berlin, Heidelberg, New York, 1977.CrossRefGoogle Scholar
[3]Γущин, A.Κ., Михайлов, B.П. [Guščin, A.K., Mikaĭlov, V.P.], “О граничных значениях B Lp, p > 1, решенийх эллиптических уравнений” [Boundary values in L p (p > 1) of solutions of elliptic equations], Mat. Sb. 108 (150) (1979), 3–21.Google Scholar
[4]Kufner, Alois, John, Oldřich and Fučík, Svatopluk, Function spaces (Noordhoff, Leyden; Academia, Prague, 1977).Google Scholar
[5]Ladyzhenskaya, Olga A. and Ural'tseva, Nina N., Linear and quasilinear elliptic equations (Mathematics in Science and Engineering, 46. Academic Press, New York and London, 1968).Google Scholar
[6]Littlewood, J.E. and Paley, R.E.A.C., “Theorems on Fourier series and power series (II)”, Proc. London Math. Soc. (2) 42 (1937), 52–89.CrossRefGoogle Scholar
[7]Михайлов, B.П. [Mikaĭlov, V.P.], “О граничных значениях решенийх эллиптических уравнений второго порядка” [The boundary values of the solutions of second order elliptic equations], Mat. Sb. 100 (142) (1976), 5–13.Google ScholarPubMed
[8]Михайлов, B.П. [Mikaĭlov, V.P.], “О граничных значениях решенийх эллиптических уравнений в областях с глалкой границей” [Boundary values of the solutions of elliptic equations in domains with a smooth boundary], Mat. Sb. 101 (143) (1976), 163–188.Google ScholarPubMed
[9]Михайлов, B.П. [Mikaĭlov, V.P.], “О задаче Дириле для эллиптического уравнения второго порядка” [The Dirichlet problem for a second order elliptic equation], Differential'nye Uravnenija 12 (1976), 1877–1891.Google ScholarPubMed
[10]Mikhailov, V.P., “On the boundary values of the solutions of elliptic equations”, Appl. Math. Optim. 6 (1980), 193–199.CrossRefGoogle Scholar
[11]Михайлов, B.П. [Mikaĭlov, V.P.], Дuфференцuалъные ураєненuя є часмных nроuзєо∂ных [Partial differential equations] (Izdat. “Nauka”, Moscow, 1976).Google Scholar
[12]Nečas, Jindřich, “On the regularity of second-order elliptic partial differential equations with unbounded Dirichlet integral”, Arch. Rational Mech. Anal. 9 (1962), 134–144.CrossRefGoogle Scholar
[13]Nečas, Jindřich, Les máthodes directes en théorie des équations elliptiques (Masson, Paris; Academia, Prague; 1967).Google Scholar
[14]Riesz, Friedrich, “Über die Randwerte einer analytischen Funktion”, Math. Z. 18 (1923), 87–95.CrossRefGoogle Scholar
[15]Stampacchia, Guido, “Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus”, Ann. Inst. Fourier (Grenoble) 15 (1965), 189–258.CrossRefGoogle Scholar
[16]Stampacchia, Guido, Équations elliptiques du second ordre á coefficients discontinus (Séminaire de Mathématiques Supérieures, 16; Été, 1965. Les Presses de l'université de Montréal, Montreal, Quebec, 1966).Google Scholar