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Lecture Notes in Mathematics

The Method of Intrinsic Scaling

A Systematic Approach to Regularity for Degenerate and Singular PDEs

Authors: Urbano, José Miguel

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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.

Reviews

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)


Table of contents (7 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-540-75932-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-540-75931-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Method of Intrinsic Scaling
Book Subtitle
A Systematic Approach to Regularity for Degenerate and Singular PDEs
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1930
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-75932-4
DOI
10.1007/978-3-540-75932-4
Softcover ISBN
978-3-540-75931-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 154
Topics