R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
- ISBN-10
- 0821833782
- ISBN-13
- 9780821833780
- Category
- Boundary value problems
- Pages
- 114
- Language
- English
- Published
- 2003
- Publisher
- American Mathematical Soc.
- Authors
- Robert Denk, Matthias Hieber, Jan Pruss
Description
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
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