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
$$extract_itex$$14$$/extract_itex$$ , with complements and extensions from a variety of sources (listed in the references), mainly
$$extract_itex$$6,7,17$$/extract_itex$$

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.

Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
제목
2014-01-07  10:30  Brownian motion on hyperbolic spaces and Martin boundary I Francois Ledrappier  129-307
2014-01-08  19:00  Quantum Factorization for Number-Theorists 김민형  129-307
2014-01-10  10:30  Brownian motion on hyperbolic spaces and Martin boundary II Francois Ledrappier  129-307
2014-01-11  10:30  Quantum Computing in a Weekend – Lecture 1,2 Artur Ekert  27-116
2014-01-12  10:30  Quantum Computing in a Weekend – Lecture 3,4 Artur Ekert  27-116
2014-01-14  10:30  Brownian motion on hyperbolic spaces and Martin boundary III Francois Ledrappier  129-307
2014-01-27  14:00  Lectures on Lefschetz fibrations Daniele Zuddas  129-301
2014-02-05  16:00  On weighted $$extract_itex$$L^2$$/extract_itex$$ estimates for solutions of the wave equation 고영우  27-220
2014-03-04  14:00-15:00  An easy criterion for randomness Teturo Kamae  27-116
2014-03-07  14:00-15:00  Fredholm Operators, Evolutionary Semigroups and Periodic Solutions of Nonlinear Periodic Systems 신정선  129-307
2014-03-11  16:30-17:30  Weight modules of algebras of twisted differential operators on the projective space Dimitar Grantcharov  27-220
2014-03-14  10:30-12:00  Weighted Fourier algebras on non-compact Lie groups and their spectrum 이훈희  129-301
2014-03-14  10:30-12:00  Weighted Fourier algebras on non-compact Lie groups and their spectrum 이훈희  129-301
2014-03-17  10:00-12:00  The Effect of Gaussian White Noise on Dynamical Systems Barbara Gentz  129-307
2014-03-17  17:00-18:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301
2014-03-17  10:30-12:00  Probabilistic Topic Models: Models and Applications 김성현  129-310
2014-03-18  14:00-15:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301
2014-03-18  16:00-17:00  Central extensions of the Thompson group T from quantization of the universal Teichmuller space 김현규  129-307
2014-03-19  16:00-17:00  The Effect of Gaussian White Noise on Dynamical Systems Barbara Gentz  129-307
2014-03-19  17:00-18:00  Topological Invariants in Disordered Systems Jean V. Bellissard  129-301