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$\mathcal{R}$-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
R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
eBook ISBN:  978-1-4704-0386-7
Product Code:  MEMO/166/788.E
List Price: $61.00
MAA Member Price: $54.90
AMS Member Price: $36.60
R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
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$\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
eBook 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.

    Readership

    Graduate students and research mathematicians interested in differential equations.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Notations and conventions
    • I. $\mathcal {R}$-boundedness and sectorial operators
    • II. Elliptic and parabolic boundary value problems
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.