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Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials
 
Michael E. Taylor University of North Carolina, Chapel Hill, NC
Front Cover for Tools for PDE
Available Formats:
Softcover ISBN: 978-0-8218-4378-9
Product Code: SURV/81.S
257 pp 
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $59.20
Electronic ISBN: 978-1-4704-1308-8
Product Code: SURV/81.S.E
257 pp 
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
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Front Cover for Tools for PDE
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Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials
Michael E. Taylor University of North Carolina, Chapel Hill, NC
Available Formats:
Softcover ISBN:  978-0-8218-4378-9
Product Code:  SURV/81.S
257 pp 
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $59.20
Electronic ISBN:  978-1-4704-1308-8
Product Code:  SURV/81.S.E
257 pp 
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $111.00
MAA Member Price: $99.90
AMS Member Price: $88.80
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 812000
    MSC: Primary 35; 42;

    This book develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials.

    A theme running throughout the work is the treatment of PDE in the presence of relatively little regularity. The first chapter studies classes of pseudodifferential operators whose symbols have a limited degree of regularity; the second chapter shows how paradifferential operators yield sharp estimates on the action of various nonlinear operators on function spaces. The third chapter applies this material to an assortment of results in PDE, including regularity results for elliptic PDE with rough coefficients, planar fluid flows on rough domains, estimates on Riemannian manifolds given weak bounds on Ricci tensor, div-curl estimates, and results on propagation of singularities for wave equations with rough coefficients. The last chapter studies the method of layer potentials on Lipschitz domains, concentrating on applications to boundary problems for elliptic PDE with variable coefficients.

    Readership

    Graduate students and research mathematicians interested in partial differential equations.

  • Table of Contents
     
     
    • Chapters
    • 1. Pseudodifferential operators with mildly regular symbols
    • 2. Paradifferential operators and nonlinear estimates
    • 3. Applications to PDE
    • 4. Layer potentials on Lipschitz surfaces
  • Additional Material
     
     
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Volume: 812000
MSC: Primary 35; 42;

This book develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials.

A theme running throughout the work is the treatment of PDE in the presence of relatively little regularity. The first chapter studies classes of pseudodifferential operators whose symbols have a limited degree of regularity; the second chapter shows how paradifferential operators yield sharp estimates on the action of various nonlinear operators on function spaces. The third chapter applies this material to an assortment of results in PDE, including regularity results for elliptic PDE with rough coefficients, planar fluid flows on rough domains, estimates on Riemannian manifolds given weak bounds on Ricci tensor, div-curl estimates, and results on propagation of singularities for wave equations with rough coefficients. The last chapter studies the method of layer potentials on Lipschitz domains, concentrating on applications to boundary problems for elliptic PDE with variable coefficients.

Readership

Graduate students and research mathematicians interested in partial differential equations.

  • Chapters
  • 1. Pseudodifferential operators with mildly regular symbols
  • 2. Paradifferential operators and nonlinear estimates
  • 3. Applications to PDE
  • 4. Layer potentials on Lipschitz surfaces
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