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

Robert Denk University of Regensburg, Regensburg, Germany
Jan Prüss University of Halle, Halle, Germany
Available Formats:
Electronic ISBN: 978-1-4704-0386-7
Product Code: MEMO/166/788.E
List Price: $61.00 MAA Member Price:$54.90
AMS Member Price: $36.60 Click above image for expanded view$\mathcal{R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type Robert Denk University of Regensburg, Regensburg, Germany Matthias Hieber University of Darmstadt, Darmstadt, Germany Jan Prüss University of Halle, Halle, Germany Available Formats:  Electronic ISBN: 978-1-4704-0386-7 Product Code: MEMO/166/788.E  List Price:$61.00 MAA Member Price: $54.90 AMS Member Price:$36.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1662003; 114 pp
MSC: Primary 35; 42;

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.

Graduate students and research mathematicians interested in differential equations.

• Chapters
• Introduction
• Notations and conventions
• I. $\mathcal {R}$-boundedness and sectorial operators
• II. Elliptic and parabolic boundary value problems
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Volume: 1662003; 114 pp
MSC: Primary 35; 42;

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.

• I. $\mathcal {R}$-boundedness and sectorial operators