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
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Apr 11, 2018  16:00-18:00  Resource theory of quantum coherence 권혁준  129-301 
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May 16, 2018  16:00-18:00  Canonical Systems on Spectral Theory 허인조  129-301 
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Oct 17, 2018  16:00-18:00  Spectra of weighted Fourier algebras on Lie groups II 이훈희  129-301 
Jun 02, 2021  16:00-18:00  Sums of free variables in symmetric spaces Éric Ricard  선택 
Aug 25, 2021  16:00-18:00  EXISTENCE AND REGULARITY FOR NONLINEAR PARABOLIC DOUBLE OBSTACLE PROBLEMS 유승진  27-116 
Sep 08, 2021  16:00-18:00  Revision of "The Invariant Subspace Problem(arXiv:2002.11533 v7 [math.GM] 5 Aug 2o21)" 이사계  129-406 
Nov 24, 2021  16:00-18:00  Matrix-valued maximal Calder'on-Zygmund operators and applications Bang Xu  선택 
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Dec 05, 2018  16:00-18:00  A canonical decomposition of strong L^2-functions 이우영  129-301