On the Solvability and the Maximal Regularity of Complete Abstract Differential Equations of Elliptic Type

Funkcialaj Ekvacioj

Volumn 47, Issue 3, 2004, Pages 423-452

  Favini, Angelo ^a   Labbas, Rabah ^b   Maingot, Stéphane ^b   Tanabe, Hiroki ^c   Yagi, Atsushi ^d  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITÉ DU HAVRE   (France)

^c OTEMON GAKUIN UNIVERSITY   (Japan)

^d OSAKA UNIVERSITY   (Japan)

Author keywords

Analytic semigroup; Boundary condition; Degenerate parabolic equation; Elliptic equation; Maximal regularity; Second order abstract differential equation

Indexed keywords

EID: 85010104591     PISSN: 05328721     EISSN: None     Source Type: Journal    
DOI: 10.1619/fesi.47.423     Document Type: Article

References (15)

1. Campiti, M., Metafune, G. and Pallara, D., Degenerate Self-adjoint Evolution Equations on the Unit Interval, Semigroup Forum 57 (1998), 1–36.
2. Da Prato, G., Abstract Differential Equations, Maximal Regularity and Linearization, Proceed. Symposia. Pura Math. 45 (1986), Part I, 359–370.
3. Da Prato, G. and Grisvard, P., Sommes d’Opérateurs Linéaires et Equations Différentielles Opérationnelles, J. Math. Pures Appl. IX Ser. 54 (1975), 305–387.
4. El Haial, A. and Labbas, R., On the Ellipticity and Solvability of Abstract Second-order Differential Equation, Electronic Journal of Differential Equations, 57 (2001), 1–18.
5. Favini, A., Labbas, R., Tanabe, H. and Yagi, A., On the Solvability of Complete Abstract Differential Equations of Elliptic Type, Funkc. Ekv., 47 (2004), 205–224.
6. Favini, A. and Romanelli, S., Analytic Semigroups on C([0,1]) Generated by some Classes of Second Order Differential Operators, Semigroup Forum 56 (1998), 367–372.
7. Favini, A. and Triggiani, R., Analytic and Gevrey Class Semigroups generated by A + iB, and Applications, in “Differential Equations in Banach Spaces”, Proceeding of the Bologna conferences, G. Dore, A. Favini, E. Obrecht, A. Venni, eds (1993), 93–114, M. Dekker, New York.
8. Goldstein, J. A., Semigroups of Linear Operators and Applications, Oxford University Press, Oxford, New York, 1985.
9. Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York, 1966.
10. Krein, S. G., Linear Differential Equations in Banach Space, Moscow, 1967; English Translation: AMS, Providence, 1971.
11. Lunardi, A., Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birk-hauser, Basel, 1995.
12. Miklavčič, M., Applied Functional Analysis and Partial Differential Equations, Word Scientific, Singapore, 1998.
13. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, Tokyo, 1983.
14. Tanabe, H., Equations of Evolution, Pitman, London, San Francisco, Melbourne, 1979.
15. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, Amsterdam, North Holland, 1978.