Maximal Regularity for Second Order Cauchy Problems is Independent of
Bollettino dell'Unione Matematica Italiana (2008)
- Volume: 1, Issue: 1, page 147-157
- ISSN: 0392-4041
Access Full Article
top
Abstract
topHow to cite
topChill, Ralph, and Srivastava, Sachi. "$L^p$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$." Bollettino dell'Unione Matematica Italiana 1.1 (2008): 147-157. <http://eudml.org/doc/290490>.
@article{Chill2008,
abstract = {If the second order problem $\ddot\{u\} + \dot\{u\} + Au = f$ has $L^p$ maximal regularity for some $p \in (1, \infty)$, then it has $L^\{p\}$ maximal regularity for every $p \in (1, \infty)$.},
author = {Chill, Ralph, Srivastava, Sachi},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {147-157},
publisher = {Unione Matematica Italiana},
title = {$L^p$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$},
url = {http://eudml.org/doc/290490},
volume = {1},
year = {2008},
}
TY - JOUR
AU - Chill, Ralph
AU - Srivastava, Sachi
TI - $L^p$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/2//
PB - Unione Matematica Italiana
VL - 1
IS - 1
SP - 147
EP - 157
AB - If the second order problem $\ddot{u} + \dot{u} + Au = f$ has $L^p$ maximal regularity for some $p \in (1, \infty)$, then it has $L^{p}$ maximal regularity for every $p \in (1, \infty)$.
LA - eng
UR - http://eudml.org/doc/290490
ER -
References
top- ACQUISTAPACE, P. - TERRENI, B., A unified approach to abstract linear non-autonomous parabolic equations, Rend. Sem. Mat. Univ. Padova, 78 (1987), 47-107. Zbl0646.34006MR934508
- ARENDT, W. - BATTY, C. J. K. - HIEBER, M. - NEUBRANDER, F., Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics, vol. 96, Birkhäuser, Basel, 2001. Zbl0978.34001MR1886588DOI10.1007/978-3-0348-5075-9
- BENEDEK, A. - CALDERÓN, A. P. - PANZONE, R., Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. USA, 48 (1962), 356-365. Zbl0103.33402MR133653
- CANNARSA, P. - VESPRI, V., On maximal regularity for the abstract Cauchy problem, Boll. Un. Mat. Ital. B, 5 (1986), 165-175. Zbl0608.35027MR841623
- CHILL, R. - SRIVASTAVA, S., -maximal regularity for second order Cauchy problems, Math. Z., 251 (2005), 751-781. Zbl1101.34043MR2190142DOI10.1007/s00209-005-0815-8
- DA PRATO, G. - GRISVARD, P., Sommes d'opérateurs linéaires et èquations différentielles opérationnelles, J. Math. Pures Appl., 54 (1975), 305-387. Zbl0315.47009MR442749
- DAUTRAY, R. - LIONS, J.-L., Analyse mathématique et calcul numérique pour les sciences et les techniques. Vol. VIII, INSTN: Collection Enseignement, Masson, Paris, 1987. MR918560
- DE SIMON, L., 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. Zbl0196.44803MR176192
- DORE, G. - VENNI, A., On the closedness of the sum of two closed operators, Math. Z., 196 (1987), 189-201. Zbl0615.47002MR910825DOI10.1007/BF01163654
- HIEBER, M., 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. Zbl0919.47021MR1725578
- LABBAS, R. - TERRENI, B., Somme d'opérateurs linéaires de type parabolique. I, Boll. Un. Mat. Ital. B (7) 1 (1987), 545-569. Zbl0627.47005MR896340
- SOBOLEVSKII, P. E., Coerciveness inequalities for abstract parabolic equations, Dokl. Akad. Nauk SSSR, 157 (1964), 52-55. MR166487
- ZEIDLER, E., Nonlinear Functional Analysis and Its Applications. I, Springer Verlag, New York, Berlin, Heidelberg, 1990. Zbl0684.47029MR1033497DOI10.1007/978-1-4612-0985-0
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.