Perturbation theorems for maximal $L_p$-regularity

Kunstmann, Peer Christian; Weis, Lutz

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 2, pp. 415-435.

[1] H. Amann, "Linear and quasilinear parabolic problems", Vol. 1: Abstract linear theory, Birkhaeuser, Basel, 1995. | MR | Zbl

[2] H. Amann - M. Hieber - G. Simonett, Bounded H∞-calculus for elliptic operators, Differential Integral Equations 7 (1994), 613-653. | Zbl

[3] Ph. Clément - S. Li, Abstract parabolic quasilinear equations and application to a groundwater flow problem, Adv. Math. Sci. Appl. 3 (1994), 17-32. | MR | Zbl

[4] Ph. Clément - B. De Pagter - F.A. Sukochev - H. Witvliet, Schauder Decomposition and Multiplier Theorems, Studia Math. 138 (2000), 135-163. | MR | Zbl

[5] Ph. Clément - J. Prüss, An operator-valued transference principle and maximal regularity on vector-valued L p-spaces, in Proc. 6th Int. Conf.on Evolution Equations, Bad Herrenalb, 1998; Marcel Dekker 2001, 67-87. | MR | Zbl

[6] E.B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995), 141-169. | MR | Zbl

[7] E.B. Davies, Limits on Lp regularity of self-adjoint elliptic operators, J. Differential Equations 135 (1997), 83-102. | MR | Zbl

[8] G. Dore, Maximal regularity in L p-spaces for an abstract Cauchy problem, to appear in Adv. Differential Equations. | MR | Zbl

[9] X.T. Duong - G. Simonett, H∞-calculus for elliptic operators with nonsmooth coefficients, Differential Integral Equations 10 (1997), 201-217. | Zbl

[10] K.-J. Engel - R. Nagel, "One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics 194", Springer, Berlin, 2000. | MR | Zbl

[11] M. Hieber - J. Prüss, Heat kernels and maximal Lp-L q estimatesforparabolic evolution equations, Commun. Partial Differerential Equations 22 (1997), 1647-1669. | MR | Zbl

[12] L. Hörmander, "The Analysis of Linear Partial Differential Operators", Vol. III, Springer, 1985. | Zbl

[ 13] P.C. Kunstmann, Maximal L p-regularity for second order elliptic operators with uniformly continuous coefficients on domains, submitted.

[14] D. Lamberton, Equations d'évolution linéaires associées a des semi-groupes de contractions dans les espaces LP, J. Funct. Anal. 72 (1987), 252-262. | MR | Zbl

[15] V.A. Liskevich, On C0-semigroups generated by elliptic second order differential expressions on Lp-spaces, Differential Integral Equations 9 (1996), 811-826. | MR | Zbl

[16] V.A. Liskevich - Yu. A. Semenov, Some problems on Markov semigroups, in Demuth, Michael (ed.) et al., Schrödinger operators, Markov semigroups, wavelet analysis, operator algebras, Berlin, Akademie Verlag, (1996), 163-217. | MR | Zbl

[17] V.A. Liskevich - H. Vogt, On Lp-spectra and essential spectra of second order elliptic operators, Proc. London Math. Soc. (3) 80 (2000), 590-610. | MR | Zbl

[18] V.G. Maz'Ya - T.O. Shaposhnikova, "Theory of multipliers in spaces of differentiable functions", Pitman, Boston, London, Melbourne, 1985. | Zbl

[19] J. Prüss - H. Sohr, Imaginary powers of elliptic second order differential operators in Lp-spaces, Hiroshima Math. J. 23 (1993), 161-192. | MR | Zbl

[20] M. Reed - B. Simon, "Methods of modem mathematical physics II", Academic Press, New York, San Francisco, London, 1975. | MR | Zbl

[21] R. Seeley, Interpolation in Lp with boundary conditions, Studia Math. 44 (1972), 47-60. | MR | Zbl

[22] L. Weis, Operator-valued Fourier Multiplier Theorems and Maximal Lp-Regularity, to appear in Math. Ann. | MR | Zbl

[23] L. Weis, A new approach to maximal Lp-regularity, in Proc. 6th Int. Conf. on Evolution Equations, Bad Herrenalb, 1998; Marcel Dekker 2001, 195-214. | MR | Zbl

[24] A. Yagi, Applications of the purely imaginary powers of operators in Hilbert spaces, J. Funct. Anal. 73 (1987), 216-231. | MR | Zbl