© 2008

The Method of Intrinsic Scaling

A Systematic Approach to Regularity for Degenerate and Singular PDEs


Part of the Lecture Notes in Mathematics book series (LNM, volume 1930)

Table of contents

  1. Front Matter
    Pages i-x
  2. The Method of Intrinsic Scaling

  3. Some Applications

  4. Back Matter
    Pages 145-150

About this book


This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs.

In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. This approach brings to light what is really essential in the method, leaving aside technical refinements needed to deal with more general equations, and is entirely self-contained.

The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions. The aim is to convince the reader of the strength of the method as a systematic approach to regularity for this important class of equations.


DEX Degenerate and singular PDEs Scratch class equation intrinsic scaling model p-Laplacian regularity set variable

Authors and affiliations

  1. 1.CMUC, Department of MathematicsUniversity of Coimbra3001-454Portugal

Bibliographic information

  • Book Title The Method of Intrinsic Scaling
  • Book Subtitle A Systematic Approach to Regularity for Degenerate and Singular PDEs
  • Authors José Miguel Urbano
  • Series Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-540-75931-7
  • eBook ISBN 978-3-540-75932-4
  • Series ISSN 0075-8434
  • Edition Number 1
  • Number of Pages X, 154
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
  • Buy this book on publisher's site
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From the reviews:

"This book concerns the regularity theory for degenerate and singular parabolic equations and the focus is on a particular subject – the Hölder continuity of solutions. … The aim of this book is to describe in details the method of intrinsic scaling … and to convince the reader of the strength of this approach to regularity, by giving evidence of its wide applicability in different situations. … The book will be very useful for researchers from different branches of mathematical physics." (Vladimir N. Grebenev, Zentralblatt MATH, Vol. 1158, 2009)