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.
제목
2022-10-05  16:00-18:00  A universal framework for entanglement detection of invariant quantum states 박상준  선택 
2022-10-04  16:00-17:00  On an extreme value law for the unipotent flow on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Keivan Mallahi Karai  선택 
2022-10-04  16:00-18:00  On the maximal Bochner-Riesz conjecture for p>2 유재현  27-116 
2022-10-04  16:00-16:30  Universality Classes in Probability Theory 변성수  129-101 
2022-10-04  16:40-17:10  Mathematical study of metastability 이중경  129-101 
2022-09-30  10:00-18:00  Introduction to Floer Homotopy: Bordism and Flow Categories 김경모  129-309 
2022-09-28  15:30-18:00  On the long-time behavior of scale-invariant solutions to the 2d Euler equation Ayman R. Said  129-301 
2022-09-28  16:00-19:00  Index-positive contact manifolds and Legendrians 권명기  129-406 
2022-09-28  16:00-18:00  A universal framework for entanglement detection of invariant quantum states 박상준  선택 
2022-09-27  15:00-16:00  Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces Shun-Jen Cheng  선택 
2022-09-23  10:00-10:50  The Watanabe-Strogatz transform and constant of motion functionals for kinetic vector models 박한솔  27-325 
2022-09-23  09:00-11:00  One Server for the Price of Two: Simple and Fast Single-Server Private Information Retrieval Vinod Vaikuntanathan  129-301 
2022-09-23  13:00-15:00  Entropy rigidity and its applications to Diophantine approximation 김태형  129-309 
2022-09-21  18:00-19:00  An overview on noncommutative maximal inequalities Guixiang Hong  선택 
2022-09-20  15:00-16:00  Relation numbers and generalized Farey graphs 김경로  129-309 
2022-09-20  16:40-17:10  An invitation to quantum groups 이신명  129-101 
2022-09-20  16:00-16:30  Introduction to representation theory 허태혁  129-101 
2022-09-16  13:00-14:30  The Markoff spectrum on the Hecke group H4 김동한  129-301 
2022-09-16  16:00-17:00  Height-moduli and lower order terms 박준용  27-325 
2022-09-13  16:00-21:00  Introduction to representations of quantum affine algebra .. file 장일승  129-406