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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.
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.
Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.
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)
"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)