Memoirs of the American Mathematical Society 2011; 118 pp; softcover Volume: 214 ISBN10: 0821849670 ISBN13: 9780821849675 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/214/1005
 The authors establish a series of optimal regularity results for solutions to general nonlinear 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. \[a(x,t,u,Du)\leq L(1+Du^{p1}), p \geq 2.\] 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 CalderónZygmund estimates for nonhomogeneous problems are achieved here. Table of Contents  Results
 Basic material, assumptions
 The \(A\)caloric approximation lemma
 Partial regularity
 Some basic regularity results and a priori estimates
 Dimension estimates
 Hölder continuity of \(u\)
 Nonlinear CalderónZygmund theory
 Bibliography
