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Resolution in hölder spaces of an elliptic problem in an unbounded domain

Part of: Elliptic equations and systems Integral transforms, operational calculus Differential and difference algebra Differential equations in abstract spaces

Published online by Cambridge University Press:  09 April 2009

Tarik Berroug ,
Rabah Labbas  and
Boubaker-Khaled Sadallah
Tarik Berroug
Affiliation:
Université du Havre LMAH, BP 540 25 rue Philippe Lebon 76058 Le Havre cedexFrance e-mail: [email protected] [email protected]
Rabah Labbas
Affiliation:
Lab. E.D.P. and Hist. of Maths Dept of Mathematics Ecole Normale Supérieure 16050-Kouba, AlgiersAlgeria e-mail: [email protected]
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Abstract

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In this paper we give new results concerning the maximal regularity of the strict solution of an abstract second-order differential equation, with non-homogeneous boundary conditions of Dirichlet type, and set in an unbounded interval. The right-hand term of the equation is a Hölder continuous function.

Keywords

Hölder Spacesabstract elliptic equation.

MSC classification

Secondary: 12H20: Abstract differential equations 34G10: Linear equations 35J25: Boundary value problems for second-order elliptic equations 44A45: Classical operational calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 81 , Issue 3 , December 2006 , pp. 387 - 404
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Balakrishnan, A. V., ‘Fractional powers of closed operators and the semi-groups generated by them’, Pacif. J. Math. 10 (1960), 419–437.CrossRefGoogle Scholar
[2]Berroug, T., Sur des Problèmes Elliptiques et Paraboliques dans les Espaces de Hölder et les Petits Hölder (Thèse de Doctorat, Université du Havre, France, 2003).Google Scholar
[3]Favini, A., Labbas, R., Maingot, S., Tanabe, H. and Yagi, A., ‘Complete abstract differential equations of elliptic type in UMD spaces’, Funkcialaj Ekvacioj, 49 (2006), 193–214.CrossRefGoogle Scholar
[4]Grisvard, P., ‘Spazi di tracce e applicazioni’, Rend. Mat. 5 (1972), 657–729.Google Scholar
[5]Krein, S. G., Linear differential equations in Banach space, Translations of Mathematical Monographs 29 (Amer. Math. Soc., Providence, RI, 1971).Google Scholar
[6]Kuyazyuk, A. V., ‘The Dirichlet problem for second order differential equations with operator coefficient’, Ukrain. Mat. Zh. 37 (1985), 256–273 (Russian).Google Scholar
[7]Labbas, R., Problèmes aux Limites pour une Equation Différentielle Abstraite du Second Ordre (Thèse d'état, Université de Nice, France, 1987).Google Scholar
[8]Lions, J. L. and Peetre, J., ‘Sur une classe d'espaces d'interpolation’, Inst. Hautes Etudes Sci. Publ. Math. 19 (1964), 5–86.Google Scholar
[9]Da Prato, G. and Grisvard, P., ‘Sommes d'opérateurs linéaires et equations différentielles opérationnelles’, J. Math. Pures Appl. 54 (1975), 305–387.Google Scholar
[10]Sinestrari, E., ‘On the abstract Cauchy problem of parabolic type in spaces of continuous functions’, J. Math. Anal. Appl. 66 (1985), 16–66.Google Scholar
[11]Sobolevskii, P. E., ‘On equations of parabolic type in Banach space’, Trudy Mosc. Mat. Obsch. 10 (1961), 297–350, (in Russian).Google Scholar
English transl.: Amer. Math. Soc. Transl. (1965), 1–62.Google Scholar
[12]Triebel, H., Interpolation theory, function spaces, differential operators (North Holland, Amsterdam, 1978).Google Scholar
[13]Veron, L., ‘Equations d'evolution semi-linéaires du second ordre dans L1’, Rev. Roumaine Math. Pures Appl. 27 (1982), 95–123.Google Scholar