The Method of Intrinsic Scaling: A Systematic Approach to Regularity for Degenerate and Singular PDEs: 1930 (Lecture Notes in Mathematics, 1930) - Softcover

Urbano, José Miguel

Softcover

ISBN 10: 354075931X ISBN 13: 9783540759317

Publisher: Springer, 2008

Synopsis

When I started giving talks on regularity theory for degenerate and sin- lar parabolic equations, a ?xed-point in the conversation during the co?- break that usually followed the seminar was the apparent contrast between the beauty of the subject and its technical di?culty. I could not agree more on the beauty part but, most of the times, overwhelmingly failed to convince my audience that the technicalities were not all that hard to follow. As in many other instances, it was the fact that the results in the literature were eventually stated and proved in their most possible generality that made the whole subject seem inexpugnable. So when I had the chance of preparing a short course on the method of intrinsic scaling, I decided to present the theory from scratch for the simplest model case of the degenerate p-Laplace equation and to leave aside technical re?nements needed to deal with more general situations. The ?rst part of the notes you are about to read is the result of that e?ort: an introductory and self-containedapproachtointrinsicscaling,aimingatbringingtolightwhatis really essential in this powerful tool in the analysis of degenerate and singular equations. As another striking feature of the method is its pervasiveness in terms of the applications, in the second part of the book, intrinsic scaling is applied to several models arising from ?ows in porous media, chemotaxis and phase transitions.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2008
• Language: English
• ISBN 10: 354075931X
• ISBN 13: 9783540759317
• Binding: Paperback
• Number of pages: 164