Maximal regularity in Lp spaces for an abstract cauchy problem

Advances in Differential Equations

Volumn 5, Issue 1-3, 2000, Pages 293-322

  Dore, Giovanni ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642408829     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. A. Benedek, A. P. Calderón, and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356-365.
2. H. Brézis, "Operateurs maximaux monotones", North-Holland, Amsterdam London, 1973.
3. P. Cannarsa and V. Vespri, On maximal Lp regularity for the abstract Cauchy problem, Boll. Un. Mat. Ital. B (6) 5 (1986), 165-175.
4. T. Coulhon and D. Lamberton, Régularité Lp pour les équations d'évolution, in B. Beauzaumy, B. Maurey and G. Pisier (Eds.), "Séminaire d'Analyse Fonctionelle 1984/1985", Publ. Math. Univ. Paris VII 26, Univérsité Paris VII, 1986, 155-165.
5. G. Da Prato and P. Grisvard, Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl. (9) 54 (1975), 305-387.
6. G. Da Prato, E. Sinestrari, Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), 285-344.
7. G. Dore, Lp regularity for abstract differential equations, in H. Komatsu (Ed.), "Functional Analysis and Related Topics, 1991 (Proceedings, Kyoto 1991)", Lecture Notes in Math. 1540, Springer, Berlin Heidelberg New York, 1993, 25-38.
8. G. Dore and A. Venni, On the closedness of the sum of two closed operators, Math. Z. 196 (1987), 189-201.
9. G. Dore, A. Venni, Maximal regularity for parabolic initial-boundary value problems in Sobolev spaces, Math. Z. 208 (1991), 297-308.
10. J. García-Cuerva and J. L. Rubio de Francia, "Weighted norm inequalities and related topics", North-Holland, Amsterdam New York Oxford, 1985.
11. Y. Giga and H. Sohr, Abstract Lp estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Funct. Anal. 102 (1991), 72-94.
12. P. Grisvard, Equations différentielles abstraites, Ann. Sci. École Norm. Sup. (4) 2 (1969), 311-395.
13. T. Kato, "Perturbation theory for linear operators", Springer, Berlin Heidelberg New York, 1966.
14. D. Lamberton, Equations d'évolutions linéaires associées 'a des semi-groupes de contractions dans les espaces Lp, J. Funct. Anal. 72 (1987), 252-262.
15. J. Lindenstrauss and L. Tzafriri, "Classical Banach spaces I, Sequence spaces", Springer, Berlin Heidelberg New York, 1977.
16. A. Mielke, Über maximale Lp-Regularität für Differentialgleichungen in Banchund Hilbert-Räumen, Math. Ann. 277 (1987), 121-133.
17. T. Miyakawa, On the initial value problem for the Navier-Stokes equations in Lp spaces, Hiroshima Math. J. 11 (1981), 9-20.
18. J. Prüss and H. Sohr, On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429-452.
19. L. de Simon, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine, Rend. Sem. Mat. Univ. Padova 34 (1964), 547-558.
20. E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl. 107 (1985), 16-66.
21. P. E. Sobolevskiǐ, Coerciveness inequalities for abstract parabolic equations (in russian), Dokl. Acad. Nauk SSSR 157 (1964), 52-55, translated in Soviet Math. Dokl. 5 (1964), 894-897.
22. H. Tanabe, "Equations of evolution", Pitman, London San Francisco Melbourne, 1979.
23. H. Triebel, "Interpolation theory, function spaces, differential operators", North-Holland, Amsterdam New York Oxford, 1978.
24. q) per operatori parabolici, in L. Modica (Ed.), "Atti del convegno su equazioni differenziali e calcolo delle variazioni", ETS, Pisa, 1985, 205-213.