Remote access

How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2294  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax

Parabolic Systems with Polynomial Growth and Regularity

About this Title

Frank Duzaar, Department Mathematik, Universität Erlangen–Nürnberg, Bismarckstrasse 1 1/2, 91054 Erlangen, Giuseppe Mingione, Dipartimento di Matematica, Università di Parma, Viale Usberti 53/a, Campus, 43100 Parma, Italy and Klaus Steffen, Mathematisches Institut, Heinrich Heine Universität Düsseldorf, Universitätstr.1 D-40225, Düsseldorf, Germany

Publication: Memoirs of the American Mathematical Society
Publication Year: 2011; Volume 214, Number 1005
ISBNs: 978-0-8218-4967-5 (print); 978-1-4704-0622-6 (online)
Published electronically: March 10, 2011
MathSciNet review: 2866816
Keywords:Parabolic systems, regularity, higher integrability, singular sets
MSC: Primary 35D10, 35K92

View full volume PDF

View other years and numbers:

Table of Contents


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


We establish a series of optimal regularity results for solutions to general non-linear parabolic systems

$\displaystyle u_t- \operatorname{div} a(x,t,u,Du)+H=0 , $

under the main assumption of polynomial growth at rate $p$ i.e.

$\displaystyle \vert a(x,t,u,Du)\vert\leq L(1+\vert Du\vert^{p-1}) ,\qquad p \geq 2 \;. $

We 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 here achieved.

References [Enhancements On Off] (What's this?)

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia