
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 |

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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 214; 2011; 118 ppMSC: 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.
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Table of Contents
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Chapters
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Acknowledgments
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Introduction
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1. Results
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2. Basic material, assumptions
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3. The $A$-caloric approximation lemma
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4. Partial regularity
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5. Some basic regularity results and a priori estimates
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6. Dimension estimates
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7. Hölder continuity of $u$
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8. Non-linear Calderón-Zygmund theory
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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