L p -maximal regularity for second order Cauchy problems

Mathematische Zeitschrift

Volumn 251, Issue 4, 2005, Pages 751-781

  Chill, Ralph ^a,c   Srivastava, Sachi ^b  

^a UNIVERSITY OF ULM   (Germany)

^b UNIVERSITY OF DELHI   (India)

^c UMR 7122   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27844477793     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00209-005-0815-8     Document Type: Article

References (38)

1. Amann, H.: Linear and quasilinear parabolic problems: abstract linear theory. Monographs in Mathematics, vol. 89, Birkhäuser, Basel, 1995
2. ∞-calculus for elliptic operators. Differential Integral Equations 7, 613-653 (1994)
3. Angenent, S.B.: Nonlinear analytic semiflows. Proc. Roy. Soc. Edinburgh 115A, 91-107 (1990)
4. Arendt, W.: Semigroups and evolution equations: functional calculus, regularity and kernel estimates. In: C.M. Dafermos, E. Feireisl (eds.), Handbook of Differential Equations, Elsevier/North Holland, 2004, pp. 1-85
5. Arendt, W., ter Elst, A.F.M.: Gaussian estimates for second order elliptic operators with boundary conditions. J. Operator Theory 38, 87-130 (1997)
6. Arosio, A., Spagnolo, S.: Global solution to the Cauchy problem for a nonlinear hyperbolic equation. In: H. Brézis, J.L. Lions, (ed.), Nonlinear Partial Differential Equations and their Applications, Collège de France seminar, vol. 6, Pitman, London, 1984, pp. 1-26
7. Bisognin, E.: Hyperbolic parabolic equations with nonlinearity of Kirchhoff-Carrier type. Rev. Mat. Univ. Complut. Madrid 8, 401-430 (1995)
8. Bourgain, J.: Some remarks on Banach spaces in which martingale difference sequences are unconditional. Ark. Math. 21, 163-168 (1983)
9. Cavalcanti, M.M., Domingos Cavalcanti, V.N., Prates Filho, J.S., Soriano, J.A.: Existence and exponential decay for a Kirchhoff-Carrier model with viscosity. J. Math. Anal. Appl. 226, 40-60 (1998)
10. Cavalcanti, M.M., Domingos Cavalcanti, V.N., Soriano, J.A.: Global existence and uniform decay rates for the Kirchhoff-Carrier model with nonlinear dissipation. Adv. Differential Equations 6, 701-730 (2001)
11. Chill, R., Fašangová, E.: Convergence to steady states of solutions of semilinear evolutionary integral equations. Calc. Var. 22, 321-342 (2005)
12. Ph. Clément, de Pagter, B., Sukochev, F.A., Witvliet, H.: Schauder decompositions and multiplier theorems. Studia Math 138, 135-168 (2000)
13. Ph. Clément, Li, S.: Abstract parabolic quasilinear problems and application to a groundwater flow problem. Adv. Math. Sci. Appl. 3, 17-32 (1994)
14. Cousin, A.T., Frota, C.L., Larkin, N.A., Medeiros, L.A.: On the abstract model of the Kirchhoff-Carrier equation. Commun. Appl. Anal. 1, 389-404 (1997)
15. Da Prato, G., Grisvard, P.: Sommes d'opérateurs linéaires et équations différentielles opérationnelles. J. Math. Pures Appl. 54, 305-387 (1975)
16. Daners, D.: Heat kernel estimates for operators with boundary conditions. Math. Nachr. 217, 13-41 (2000)
17. Denk, R., Hieber, M., Prüss, J.: ℛ-Boundedness, fourier multipliers and problems of elliptic and parabolic type. Memoirs Amer. Math. Soc., vol. 166, Amer. Math. Soc., Providence, R.I., 2003
18. Duong, X.T., Robinson, D.W.: Semigroup kernels, Poisson kernels and holomorphic functional calculus. J. Funct. Anal. 142, 89-129 (1996)
19. Escher, J., Prüss, J., Simonett, G.: A new approach to the regularity of solutions of parabolic equations. Evolution Equations: Proceedings in Honor of J. A. Goldstein's 60th Birthday, Marcel Dekker, New York, 2003, pp. 167-190
20. Haase, M.: The Functional Calculus for Sectorial Operators. Birkhäuser Verlag, Basel, 2005, book manuscript to appear
21. p spaces. In: Günter Lumer et al. (ed.), Partial differential equations, models in physics and biology, Contributions to the conference held in Han-sur-Lesse, Belgium (1993), Akademie Verlag, Berlin, 1994, pp. 166-173
22. ∞ calculus for second order elliptic operators in divergence form. In: M. Demuth et al. (ed.), Partial differential operators and mathematical physics, International conference in Holzhau, Germany (1994), Operator Theory, Adv. Appl., vol. 78, Birkhäuser Verlag, Basel, 1995, pp. 166-173
23. ∞-calculus and sums of closed operators. Math. Ann. 321, 319-345 (2001)
24. Keyantuo, V., Lizama, C.: Fourier multipliers and integro-differential equations in Banach spaces. J. London Math. Soc. 69, 737-750 (2004)
25. ∞ functional calculus. In: M. Iannelli, R. Nagel, S. Piazzera (eds.), Proceedings of the Autumn School on Evolution Equations and Semigroups, Levico Lectures, vol. 69, Springer, Heidelberg, Berlin, 2004, pp. 65-320
26. Lunardi, A.: Analytic semigroups and optimal regularity in parabolic problems. Progress in Nonlinear Differential Equations and Their Applications, vol. 16, Birkhäuser, Basel, 1995
27. Martinez, C., Sanz, M.: The theory of fractional powers of operators. North Holland Mathematical Studies, vol. 187, Elsevier, Amsterdam, London, New York, 2001
28. Medeiros, L.A., Miranda, M.M.: On a nonlinear wave equation with damping. Rev. Mat. Univ. Complut. Madrid 3, 613-629 (1990)
29. de Pagter, B., Witvliet, H.: Unconditional decompositions and U M D-spaces. Publications Mathématiques de l'UFR Sciences et Techniques de Besançon, Fascicule 16, 79-111 (1998)
30. Pisier, G.: Some results on Banach spaces without local unconditional structure. Compositio Math 37, 3-19 (1978)
31. Prüss, J.: Evolutionary integral equations and applications. Monographs in Mathematics, vol. 87, Birkhäuser, Basel, 1993
32. p-spaces. Conf. Semin. Mat. Univ. Bari 285, 1-39 (2003)
33. Reed, M., Simon, B.: Methods of modern mathematical physics, I: functional analysis. Second edition, Academic Press, New York, 1980
34. Tanaka, N.: Abstract Cauchy problems for quasi-linear evolution equations in the sense of Hadamard. Proc. London Math. Soc. 89, 123-160 (2004)
35. Triebel, H.: Theory of function spaces. Birkhäuser, Basel, 1983
36. p-regularity. Math. Ann. 319, 735-758 (2001)
37. Yamazaki, T.: Bounded solutions of quasilinear hyperbolic equations of Kirchhoff type with dissipative and forcing terms. Funkcialaj Ekvacioj 43, 511-528 (2000)
38. Zeidler, E.: Nonlinear functional analysis and its applications, I. Springer, New York, Berlin, Heidelberg, 1990