The Method of Intrinsic Scaling

A Systematic Approach to Regularity for Degenerate and Singular PDEs

  • José Miguel Urbano

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

  • José Miguel Urbano
    • 1
  1. 1.CMUC, Department of MathematicsUniversity of Coimbra3001-454Portugal

Bibliographic information