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
Jun 20, 2024  15:30-16:30  Geodesic flats, Ramanujan complex and Zeta functions 권상훈  129-301 
Apr 17, 2015  16:00-17:00  Asymptotic behavior of shock waves in hyperbolic conservation laws 권봉석  27-116 
Oct 11, 2016  16:00-18:00  Quasi-neutral limit for the Euler-Poisson system 권봉석  27-116 
Jul 30, 2024  16:30-17:30  Delta-shock for the Euler-Poisson system 권봉석  129-104 
Jun 27, 2023  17:00-18:00  EULER-POISSON SYSTEM AND RELATED PROBLEMS 권봉석  27-116 
Nov 18, 2015  14:00-16:00  Classification of smooth Schubert varieties of the rational homogeneous manifold of type ($F_4$ ,$α_4$ ) file 권민혁  129-307 
Jul 08, 2021  16:30-18:00  An explicit computation of wrapped Floer homology ring via Seidel maps 권명기  27-325 
Sep 28, 2022  16:00-19:00  Index-positive contact manifolds and Legendrians 권명기  129-406 
Apr 14, 2023  15:00-16:00  From De Giorgi's minimizing movements to gradient flows 권도현  27-325 
Oct 30, 2024  15:00-17:30  De Giorgi's minimizing movements, optimal transport, and bilevel optimization 권도현  27-220 
Nov 01, 2022  16:00-17:00  Approaches to the alleviation of the burden of learning for Weakly Supervised Object Localization 구본경  129-301 
Oct 22, 2019  16:00-17:00  Well-posedness issues of some dispersive equations under the periodic boundary condition file 곽철광  27-116 
Oct 08, 2024  17:00-18:00  Periodic fifth-order modified KdV equation 곽철광  27-116 
Oct 22, 2024  16:40-17:10  [Rookies Pitch] Graphs, Surfaces, and their Symmetries 곽상훈  129-101 
Nov 26, 2019  16:00-17:00  A sharp square function estimate for the cone in R^3 고혜림  27-116 
Oct 17, 2023  17:00-18:00  A Sharp square function estimate for the moment curves in R^d 고혜림  27-116 
Dec 22, 2016  15:00-17:00  Cohomology of quantum groups at roots of unity 고한경  129-104 
Jul 16, 2024  10:30-12:30  Highest weight categories and quasi-hereditary algebras 고한경  129-301 
Jul 18, 2024  10:30-13:00  Highest weight categories and quasi-hereditary algebras 고한경  129-301 
Jun 09, 2016  15:00-16:00  Existence of multiple positive solutions for a singular p(x)-Laplacian equation file 고은경  129-307