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.
Subject
Mar 26, 2019  17:30-18:20  Pointwise convergence along restricted directions for the fractional Schrödinger equation Shobu Shiraki  27-116
Mar 20, 2019  16:00-17:30  Quantum systems associated to projective representations on abelian groups 이훈희  129-301
Mar 19, 2019  01:30-02:30  The Farey Sequence Next-Term Algorithm, and the Boca-Cobeli-Zaharescu Map Analogue for Hecke Triangle Groups G_q(1) Diaaeldin Taha  선택
Mar 19, 2019  16:00-17:00  Transference of Bilinear Restriction Estimates to Quadratic Variation Norms 홍석창  27-116
Mar 19, 2019  16:30-17:30  The Farey Sequence Next-Term Algorithm, and the Boca-Cobeli-Zaharescu Map Analogue for Hecke Triangle Groups Gq (2) Diaaeldin Taha  27-325
Mar 15, 2019  11:00-12:00  The Dirichlet-to-Neumann operator associated with the Total Variational Flow operator Daniel Hauer  27-220
Mar 15, 2019  16:00-17:00  A quantitative analysis of the level lowering congruences 김찬호  27-325
Mar 13, 2019  16:00-17:30  Entangled edge states of corank one with positive partial transposes 김영훈  129-301
Feb 18, 2019  14:00-17:00  Recent Advances and New Challenges for Distributed Cooperative Control and Optimization in Complex Networks Wenwu Yu  27-220
Feb 14, 2019  14:00-16:00  Root numbers 한겨울  27-116
Jan 31, 2019  11:00-12:00  Non - Euclidean versions of some classical theorems in the low-dimensional geometry Alexander Mednykh  129-301
Jan 30, 2019  14:00-16:00  The Calderon-Zygmund type estimate for elliptic equations with minimal regular datum. Shuang Liang  27-325
Jan 24, 2019  14:00-15:00  Root numbers 한겨울  27-116
Jan 23, 2019  16:00-17:00  Regularity for elliptic equations in heterogeneous media Li-Ming Yeh  129-301
Jan 23, 2019  15:00-16:00  Nitsche-eXtended finite element methods for optimal control problems of elliptic interface equations Xiaoping Xie  129-301
Jan 18, 2019  14:00-16:00  Macdonald Polynomials: Representation Theory and Combinatorics Cristian Lenart  129-301
Jan 16, 2019  14:00-16:00  Macdonald Polynomials: Representation Theory and Combinatorics Cristian Lenart  129-406
Jan 14, 2019  14:00-16:00  Macdonald Polynomials: Representation Theory and Combinatorics Cristian Lenart  129-406
Jan 04, 2019  16:30-17:30  Birational geometry of moduli spaces of curves: a half-century of questions, conjectures and answers Prof. Ian Morrison  129-301
Jan 04, 2019  14:00-15:00  "Can you play a fair game of craps with a loaded pair of dice?'' and related problems about factorization in $$extract_itex$$mathbbR^ge0 $$x$$$$/extract_itex$$ Prof. Ian Morrison  129-301