Chill, Srivastava: $L^p$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$

Chill, Ralph and Srivastava, Sachi:
$L^p$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.1, p. 147-157, (English)
pdf (441 Kb), djvu (110 Kb). | MR 2388002 | Zbl 1210.34078

Sunto

Si prova che se il problema del secondo ordine $\ddot{u} + \dot{u} + Au = f$ ha regolarità massimale $L^p$ per qualche $p \in (1, \infty)$ allora ha regolarità massimale $L^p$ per ogni $p \in (1, \infty)$.

Referenze Bibliografiche

[1] P. ACQUISTAPACE - B. TERRENI, A unified approach to abstract linear non-autonomous parabolic equations, Rend. Sem. Mat. Univ. Padova, 78 (1987), 47-107. | fulltext EuDML | MR 934508 | Zbl 0646.34006

[2] W. ARENDT - C. J. K. BATTY - M. HIEBER - F. NEUBRANDER, Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, vol. 96, Birkhäuser, Basel, 2001. | fulltext (doi) | MR 1886588 | Zbl 0978.34001

[3] A. BENEDEK - A. P. CALDERÓN - R. PANZONE, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. USA, 48 (1962), 356-365. | MR 133653 | Zbl 0103.33402

[4] P. CANNARSA - V. VESPRI, On maximal $L^p$ regularity for the abstract Cauchy problem, Boll. Un. Mat. Ital. B, 5 (1986), 165-175. | MR 841623 | Zbl 0608.35027

[5] R. CHILL - S. SRIVASTAVA, $L^p$-maximal regularity for second order Cauchy problems, Math. Z., 251 (2005), 751-781. | fulltext (doi) | MR 2190142 | Zbl 1101.34043

[6] G. DA PRATO - P. GRISVARD, Sommes d'opérateurs linéaires et èquations différentielles opérationnelles, J. Math. Pures Appl., 54 (1975), 305-387. | MR 442749 | Zbl 0315.47009

[7] R. DAUTRAY - J.-L. LIONS, Analyse mathématique et calcul numérique pour les sciences et les techniques. Vol. VIII, INSTN: Collection Enseignement, Masson, Paris, 1987. | MR 918560

[8] 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. | fulltext EuDML | MR 176192 | Zbl 0196.44803

[9] G. DORE - A. VENNI, On the closedness of the sum of two closed operators, Math. Z., 196 (1987), 189-201. | fulltext EuDML | fulltext (doi) | MR 910825 | Zbl 0615.47002

[10] M. HIEBER, Operator valued Fourier multipliers, Topics in nonlinear analysis. The Herbert Amann anniversary volume (J. Escher, G. Simonett, eds.), Progress in Nonlinear Differential Equations and Their Applications, vol. 35, Birkhauser Verlag, Basel, 1999, pp. 363-380. | MR 1725578 | Zbl 0919.47021

[11] R. LABBAS - B. TERRENI, Somme d'opérateurs linéaires de type parabolique. I, Boll. Un. Mat. Ital. B (7) 1 (1987), 545-569. | MR 896340 | Zbl 0627.47005

[12] P. E. SOBOLEVSKII, Coerciveness inequalities for abstract parabolic equations, Dokl. Akad. Nauk SSSR, 157 (1964), 52-55. | MR 166487

[13] E. ZEIDLER, Nonlinear Functional Analysis and Its Applications. I, Springer Verlag, New York, Berlin, Heidelberg, 1990. | fulltext (doi) | MR 1033497 | Zbl 0684.47029

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche