An error was encountered while trying to add the item to the cart. Please try again.
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
Available Formats:
Electronic 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 Click above image for expanded view 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  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.

• 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 reviewers who would like to review an AMS book
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 reviewers who would like to review an AMS book
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.