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
Sep 03, 2021  10:30-12:00  Large deviation principle for heavy tailed random variables III 이창한  선택 
Apr 02, 2021  10:30-12:00  Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types. 오세진  선택 
Apr 21, 2016  10:30-12:30  Stability of pencils of quadrics and nets of quadrics 변상호  129-301 
Jan 31, 2017  10:30-12:30  Hodge theory 이상욱  129-301 
Jun 03, 2021  10:30-12:30  Locking-free and locally-conservative enriched Galerkin methods for linear poroelasticity 이상현  129-310 
Jan 27, 2022  10:30-12:30  Simultaneous determination of shape and refractive index of a deformed microjet cavity from its resonances 문송기  선택 
Sep 30, 2021  10:30-12:40  Schur-Weyl duality, old and new & Quantum symmetric pairs and Schur-type dualities Chun-Ju Lai  선택 
Oct 03, 2018  10:30-13:30  Reidemeister torsion of a homology 3-sphere Teruaki Kitano  129-310 
Feb 19, 2018  10:30-16:30  K-theory and T-duality of topological phases Guo Chuan Thiang  129-301 
Feb 19, 2020  10:30-17:00  Quantum unipotent coordinate algebras and dual canonical bases Yoshiyuki Kimura  129-104 
Feb 20, 2020  10:30-17:00  Quantum unipotent coordinate algebras and dual canonical bases Yoshiyuki Kimura  129-104 
Feb 18, 2020  10:30-17:30  Quantum unipotent coordinate algebras and dual canonical bases Yoshiyuki Kimura  129-104 
Dec 04, 2017  10:45-12:15  해석학특강 학기말 조별 발표   27-220 
Dec 06, 2017  10:45-12:15  해석학특강 학기말 조별 발표   27-220 
May 18, 2017  10:55-11:55  A Multivariate extreme value law (EVL) for maximal geodesic windings around distinct cusps Maxim Kirsebom  129-406 
Jun 04, 2022  11:00-11:30  Global Sobolev regularity for general type of elliptic equations with measure data Pilsoo Shin  27-325 
Nov 28, 2014  11:00-11:50  Stochastic modeling of biochemical networks Hye-Won Kang  129-104 
Aug 14, 2018  11:00-11:50  On high-order methods for moment-closure approximations of kinetic Boltzmann equations James Rossmanith  27-220 
Jan 20, 2015  11:00-12:00  Determinant formula for K-theory of Grassmannians III Tomoo Matsumura  129-301 
May 15, 2015  11:00-12:00  Boundary layer for compressible flow Tong Yang  27-325