Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
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
Front Cover for Parabolic Systems with Polynomial Growth and Regularity
Available Formats:
Electronic ISBN: 978-1-4704-0622-6
Product Code: MEMO/214/1005.E
118 pp 
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Front Cover for Parabolic Systems with Polynomial Growth and Regularity
Click above image for expanded view
  • Front Cover for Parabolic Systems with Polynomial Growth and Regularity
  • Back Cover for Parabolic Systems with Polynomial Growth and Regularity
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
Available Formats:
Electronic ISBN:  978-1-4704-0622-6
Product Code:  MEMO/214/1005.E
118 pp 
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2142011
    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
  • Request Review Copy
  • Get Permissions
Volume: 2142011
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
Please select which format for which you are requesting permissions.