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Elliptic Regularization and Partial Regularity for Motion by Mean Curvature
 
Elliptic Regularization and Partial Regularity for Motion by Mean Curvature
eBook ISBN:  978-1-4704-0097-2
Product Code:  MEMO/108/520.E
List Price: $40.00
MAA Member Price: $36.00
AMS Member Price: $24.00
Elliptic Regularization and Partial Regularity for Motion by Mean Curvature
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Elliptic Regularization and Partial Regularity for Motion by Mean Curvature
eBook ISBN:  978-1-4704-0097-2
Product Code:  MEMO/108/520.E
List Price: $40.00
MAA Member Price: $36.00
AMS Member Price: $24.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1081994; 90 pp
    MSC: Primary 35; 53; 82;

    This monograph considers (singular) surfaces moving by mean curvature, combining tools of geometric measure theory with “viscosity solution” techniques. Employing the geometrically natural concept of “elliptic regularization”, Ilmanen establishes the existence of these surfaces. The ground-breaking work of Brakke, combined with the recently developed “level-set” approach, yields surfaces moving by mean curvature that are smooth almost everywhere. The methods developed here should form a foundation for further work in the field. This book is also noteworthy for its especially clear exposition and for an introductory chapter summarizing the key compactness theorems of geometric measure theory.

    Readership

    Geometric measure theorists as well as mathematicians involved in partial differential equations and phase transitions.

  • Table of Contents
     
     
    • Chapters
    • I. Elliptic regularization
    • II. Partial regularity in codimension one
  • 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: 1081994; 90 pp
MSC: Primary 35; 53; 82;

This monograph considers (singular) surfaces moving by mean curvature, combining tools of geometric measure theory with “viscosity solution” techniques. Employing the geometrically natural concept of “elliptic regularization”, Ilmanen establishes the existence of these surfaces. The ground-breaking work of Brakke, combined with the recently developed “level-set” approach, yields surfaces moving by mean curvature that are smooth almost everywhere. The methods developed here should form a foundation for further work in the field. This book is also noteworthy for its especially clear exposition and for an introductory chapter summarizing the key compactness theorems of geometric measure theory.

Readership

Geometric measure theorists as well as mathematicians involved in partial differential equations and phase transitions.

  • Chapters
  • I. Elliptic regularization
  • II. Partial regularity in codimension one
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.