Abstract: The mini-course is an introductory and self-contained approach to the method of intrinsic scaling, aiming at bringing to light what is really essential in this powerful tool in the analysis of degenerate and singular equations. The theory is presented from scratch for the simplest model case of the degenerate p-Laplace equation, leaving aside
technical renements needed to deal with more general situations. A striking feature of the method is its pervasiveness in terms of the applications and I hope to convince the audience of its strength as a systematic approach to regularity for an important and relevant class of nonlinear partial dierential equations. I will extensively follow my book
14 , with complements and extensions from a variety of sources (listed in the references), mainly
6,7,17

10/16()09:00 11:00 Lecture I.
An impressionist history lesson: from Hilbert's 19th problem to DeGiorgi-Nash-Moser theory; the quasilinear case { contributions from the Russian school; enters DiBenedetto { the method of intrinsic scaling.

10/17()09:00- 11:00 Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

10/19()09:00 -11:00 Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

10/22()09:00 -11:00 Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

10/23()09:00 -11:00 Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
Subject
Jan 07, 2014  10:30  Brownian motion on hyperbolic spaces and Martin boundary I Francois Ledrappier  129-307 
Jan 08, 2014  19:00  Quantum Factorization for Number-Theorists 김민형  129-307 
Jan 10, 2014  10:30  Brownian motion on hyperbolic spaces and Martin boundary II Francois Ledrappier  129-307 
Jan 11, 2014  10:30  Quantum Computing in a Weekend – Lecture 1,2 Artur Ekert  27-116 
Jan 12, 2014  10:30  Quantum Computing in a Weekend – Lecture 3,4 Artur Ekert  27-116 
Jan 14, 2014  10:30  Brownian motion on hyperbolic spaces and Martin boundary III Francois Ledrappier  129-307 
Jan 27, 2014  14:00  Lectures on Lefschetz fibrations file Daniele Zuddas  129-301 
Feb 05, 2014  16:00  On weighted $L^2$ estimates for solutions of the wave equation file 고영우  27-220 
Mar 04, 2014  14:00-15:00  An easy criterion for randomness Teturo Kamae  27-116 
Mar 07, 2014  14:00-15:00  Fredholm Operators, Evolutionary Semigroups and Periodic Solutions of Nonlinear Periodic Systems file 신정선  129-307 
Mar 11, 2014  16:30-17:30  Weight modules of algebras of twisted differential operators on the projective space Dimitar Grantcharov  27-220 
Mar 14, 2014  10:30-12:00  Weighted Fourier algebras on non-compact Lie groups and their spectrum 이훈희  129-301 
Mar 14, 2014  10:30-12:00  Weighted Fourier algebras on non-compact Lie groups and their spectrum 이훈희  129-301 
Mar 17, 2014  10:00-12:00  The Effect of Gaussian White Noise on Dynamical Systems Barbara Gentz  129-307 
Mar 17, 2014  17:00-18:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301 
Mar 17, 2014  10:30-12:00  Probabilistic Topic Models: Models and Applications 김성현  129-310 
Mar 18, 2014  14:00-15:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301 
Mar 18, 2014  16:00-17:00  Central extensions of the Thompson group T from quantization of the universal Teichmuller space 김현규  129-307 
Mar 19, 2014  16:00-17:00  The Effect of Gaussian White Noise on Dynamical Systems Barbara Gentz  129-307 
Mar 19, 2014  17:00-18:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301