**Memoirs of the American Mathematical Society**

2003;
114 pp;
Softcover

MSC: Primary 35; 42;

Print ISBN: 978-0-8218-3378-0

Product Code: MEMO/166/788

List Price: $61.00

AMS Member Price: $36.60

MAA Member Price: $54.90

**Electronic ISBN: 978-1-4704-0386-7
Product Code: MEMO/166/788.E**

List Price: $61.00

AMS Member Price: $36.60

MAA Member Price: $54.90

# \(\mathcal{R}\)-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

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*Robert Denk; Matthias Hieber; Jan Prüss*

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.

#### Readership

Graduate students and research mathematicians interested in differential equations.

#### Table of Contents

# Table of Contents

## $\mathcal{R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type

- Contents v6 free
- Introduction 110 free
- Notations and Conventions 312 free
- I: R-Boundedness and Sectorial Operators 514
- II: Elliptic and Parabolic Boundary Value Problems 5766
- Notes 108117
- References 111120