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
Nov 07, 2014  10:30-12:00  Matrix inner functions 황인성  129-301 
Sep 25, 2015  14:00-17:00  Intensive Lecture on matrix functions of bounded type 황인성  27-116 
Oct 02, 2015  10:30-12:00  Douglas-Shapiro-Shields factorizations 황인성  129-301 
Oct 30, 2015  14:00-15:00  Coprime factorizations of bounded type functions 황인성  27-116 
Apr 12, 2017  16:00-17:30  On the n×r inner matrix function file 황인성  129-301 
Jun 15, 2018  15:00-17:00  Intensive Lecture on Operator Theory - Vector-valued Hardy classes (I) 황인성  27-116 
Jun 22, 2018  15:00-17:00  Intensive Lecture on Operator Theory - Vector-valued Hardt classes (II) 황인성  27-116 
Nov 07, 2018  16:00-17:30  The kernel of Hankel operators 황인성  129-301 
Oct 20, 2017  16:30-17:30  Teaching Human Intelligence to AI 황승원  129-301 
Feb 23, 2017  16:00-18:00  the Alexandrov-Bakelman-Pucci maximum principle for Elliptic PDEs in the plane 황숙정  129-301 
Dec 30, 2021  10:00-11:30  Regularity and existence of weak solutions of porous medium equation with a divergence type of drift II 황숙정  선택 
Dec 28, 2021  10:00-11:30  Regularity and existence of weak solutions of porous medium equation with a divergence type of drift I 황숙정  선택 
Nov 26, 2021  13:30-14:00  Emergent behaviors of Lohe hermitian sphere particles under time-delayed interactions 황규영  27-220 
Apr 17, 2015  11:00-12:00  Almost sure local wellposedness of energy critical fractional Schr 황경하  129-310 
Jul 05, 2016  15:00-16:00  Noncommutative Mirror Functors 홍한솔  129-301 
Nov 29, 2019  11:00-13:00  Koszul duality in Floer theory 홍한솔  129-307 
Dec 22, 2015  16:00-18:00  Global well-posedness of the NLS system for infinitely many fermions 홍영훈  27-116 
Nov 01, 2016  16:00-18:00  An extremizer for the kinetic energy inequality 홍영훈  27-116 
Oct 30, 2018  16:30-18:00  Continuum limit for discrete nonlinear Schrödinger equations 홍영훈  27-116 
May 21, 2015  11:00-12:00  Numerical simulations of the primitive equations with humidity and saturations above mountain 홍영준  27-325