Overview
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.
Full Product Details
Author: José Miguel Urbano
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2008 ed.
Volume: 1930
Dimensions:
Width: 21.00cm
, Height: 0.90cm
, Length: 29.70cm
Weight: 0.540kg
ISBN: 9783540759317
ISBN 10: 354075931
Pages: 154
Publication Date: 29 May 2008
Audience:
College/higher education
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: In Print
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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 Holder 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)
<p>From the reviews: <p><p> This book concerns the regularity theory for degenerate and singular parabolic equations and the focus is on a particular subject the H lder 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)
From the reviews: This book concerns the regularity theory for degenerate and singular parabolic equations and the focus is on a particular subject - the Hoelder 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)
