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Parabolic Systems with Polynomial Growth and Regularity
 
Frank Duzaar Universität Erlangen-Nürnberg, Erlangen, Germany
Giuseppe Mingione Università di Parma, Parma, Italy
Klaus Steffen Heinrich-Heine-Universität, Düsseldorf, Germany
Parabolic Systems with Polynomial Growth and Regularity
eBook ISBN:  978-1-4704-0622-6
Product Code:  MEMO/214/1005.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Parabolic Systems with Polynomial Growth and Regularity
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Parabolic Systems with Polynomial Growth and Regularity
Frank Duzaar Universität Erlangen-Nürnberg, Erlangen, Germany
Giuseppe Mingione Università di Parma, Parma, Italy
Klaus Steffen Heinrich-Heine-Universität, Düsseldorf, Germany
eBook ISBN:  978-1-4704-0622-6
Product Code:  MEMO/214/1005.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2142011; 118 pp
    MSC: Primary 35;

    The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems \[ u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,\] under the main assumption of polynomial growth at rate \(p\) i.e. \[|a(x,t,u,Du)|\leq L(1+|Du|^{p-1}), p \geq 2.\] They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderón-Zygmund estimates for non-homogeneous problems are achieved here.

  • Table of Contents
     
     
    • Chapters
    • Acknowledgments
    • Introduction
    • 1. Results
    • 2. Basic material, assumptions
    • 3. The $A$-caloric approximation lemma
    • 4. Partial regularity
    • 5. Some basic regularity results and a priori estimates
    • 6. Dimension estimates
    • 7. Hölder continuity of $u$
    • 8. Non-linear Calderón-Zygmund theory
  • 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: 2142011; 118 pp
MSC: Primary 35;

The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems \[ u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,\] under the main assumption of polynomial growth at rate \(p\) i.e. \[|a(x,t,u,Du)|\leq L(1+|Du|^{p-1}), p \geq 2.\] They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderón-Zygmund estimates for non-homogeneous problems are achieved here.

  • Chapters
  • Acknowledgments
  • Introduction
  • 1. Results
  • 2. Basic material, assumptions
  • 3. The $A$-caloric approximation lemma
  • 4. Partial regularity
  • 5. Some basic regularity results and a priori estimates
  • 6. Dimension estimates
  • 7. Hölder continuity of $u$
  • 8. Non-linear Calderón-Zygmund theory
Review Copy – for publishers of book reviews
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