Memoirs of the American Mathematical Society 2013; 143 pp; softcover Volume: 221 ISBN10: 0821889753 ISBN13: 9780821889756 List Price: US$76 Individual Members: US$45.60 Institutional Members: US$60.80 Order Code: MEMO/221/1041
 The aim of the paper is twofold. On one hand the authors want to present a new technique called \(p\)caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classical tool to prove linearization and regularity results for vectorial problems. Here the authors develop a very far reaching version of this general principle devised to linearize general degenerate parabolic systems. The use of this result in turn allows the authors to achieve the subsequent and main aim of the paper, that is, the implementation of a partial regularity theory for parabolic systems with degenerate diffusion of the type \(\partial_t u  \mathrm{div} a(Du)=0\), without necessarily assuming a quasidiagonal structure, i.e. a structure prescribing that the gradient nonlinearities depend only on the the explicit scalar quantity. Table of Contents  Introduction and results
 Technical preliminaries
 Tools for the \(p\)caloric approximation
 The \(p\)caloric approximation lemma
 Caccioppoli and Poincaré type inequalities
 Approximate \(\mathcal A\)caloricity and \(p\)caloricity
 DiBenedetto & Friedman regularity theory revisited
 Partial gradient regularity in the case \(p>2\)
 The case \(p<2\)
 Partial Lipschitz continuity of \(u\)
 Bibliography
