Fourier multipliers and maximal Lp-regularity for differential operators with VMO coefficients

Fourier Multiplier theorems play an important role in the analysis of elliptic and parabolic problems. In particular, it turned out that operator-valued Fourier Multipliers are deeply connected with the property of Maximal Regularity for linear parabolic equations. Maximal Regularity results are known to be very useful for nonlinear parabolic problems. This is certainly one reason why results in this direction gained considerable interest in recent years. In this context, one has to look for minimal smoothness assumptions on the coefficients of the differential operators involved. Therefore, in this book, operator-valued Fourier Multipliers are investigated first. Then differential operators in nondivergence form having discontinuous coefficients are discussed.