Perturbation theorems for maximal $L_p$-regularity

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1. [1] H. Amann, "Linear and quasilinear parabolic problems", Vol. 1: Abstract linear theory, Birkhaeuser, Basel, 1995. Zbl0819.35001MR1345385
2. [2] H. Amann - M. Hieber - G. Simonett, Bounded H∞-calculus for elliptic operators, Differential Integral Equations7 (1994), 613-653. Zbl0799.35060
3. [3] PH. Clément - S. Li, Abstract parabolic quasilinear equations and application to a groundwater flow problem, Adv. Math. Sci. Appl.3 (1994), 17-32. Zbl0811.35040MR1287921
4. [4] PH. Clément - B. De Pagter - F.A. Sukochev - H. Witvliet, Schauder Decomposition and Multiplier Theorems, Studia Math. 138 (2000), 135-163. Zbl0955.46004MR1749077
5. [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 Dekker2001, 67-87. Zbl0988.35100MR1816437
6. [6] E.B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal.132 (1995), 141-169. Zbl0839.35034MR1346221
7. [7] E.B. Davies, Limits on Lp regularity of self-adjoint elliptic operators, J. Differential Equations135 (1997), 83-102. Zbl0871.35020MR1434916
8. [8] G. Dore, Maximal regularity in L p-spaces for an abstract Cauchy problem, to appear in Adv. Differential Equations. Zbl0993.34058MR1734544
9. [9] X.T. Duong - G. Simonett, H∞-calculus for elliptic operators with nonsmooth coefficients, Differential Integral Equations10 (1997), 201-217. Zbl0892.47017
10. [10] K.-J. Engel - R. Nagel, "One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics 194", Springer, Berlin, 2000. Zbl0952.47036MR1721989
11. [11] M. Hieber - J. Prüss, Heat kernels and maximal Lp-L q estimatesforparabolic evolution equations, Commun. Partial Differerential Equations22 (1997), 1647-1669. Zbl0886.35030MR1469585
12. [12] L. Hörmander, "The Analysis of Linear Partial Differential Operators", Vol. III, Springer, 1985. Zbl0601.35001
13. [ 13] P.C. Kunstmann, Maximal L p-regularity for second order elliptic operators with uniformly continuous coefficients on domains, submitted. Zbl1230.35033
14. [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. Zbl0621.47039MR886813
15. [15] V.A. Liskevich, On C0-semigroups generated by elliptic second order differential expressions on Lp-spaces, Differential Integral Equations9 (1996), 811-826. Zbl0852.47018MR1401439
16. [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. Zbl0854.47027MR1409835
17. [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. Zbl1053.35114MR1744777
18. [18] V.G. Maz'ya - T.O. Shaposhnikova, "Theory of multipliers in spaces of differentiable functions", Pitman, Boston, London, Melbourne, 1985. Zbl0645.46031
19. [19] J. Prüss - H. Sohr, Imaginary powers of elliptic second order differential operators in Lp-spaces, Hiroshima Math. J.23 (1993), 161-192. Zbl0790.35023MR1211773
20. [20] M. Reed - B. Simon, "Methods of modem mathematical physics II", Academic Press, New York, San Francisco, London, 1975. Zbl0308.47002MR493420
21. [21] R. Seeley, Interpolation in Lp with boundary conditions, Studia Math.44 (1972), 47-60. Zbl0237.46041MR315432
22. [22] L. Weis, Operator-valued Fourier Multiplier Theorems and Maximal Lp-Regularity, to appear in Math. Ann. Zbl0989.47025MR1825406
23. [23] L. Weis, A new approach to maximal Lp-regularity, in Proc. 6th Int. Conf. on Evolution Equations, Bad Herrenalb, 1998; Marcel Dekker2001, 195-214. Zbl0981.35030MR1818002
24. [24] A. Yagi, Applications of the purely imaginary powers of operators in Hilbert spaces, J. Funct. Anal.73 (1987), 216-231. Zbl0621.47024MR890664