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

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.
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Dec 03, 2021  10:00-12:00  Analysis for Elliptic Equations #4 Lihe Wang  선택 
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Apr 07, 2014  14:00-15:00  Dfferential Games of Evasion and Pontryagin\'s Lemma Lev Yugay  129-307 
Apr 27, 2017  13:00-15:00  Information Asymmetry in Mathematical Finance Lee, Kiseop  129-104 
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Mar 16, 2021  11:00-12:00  Transfer operators and limit laws for typical cocycles Kiho Park  선택 
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Sep 18, 2019  16:00-17:00  Fermat's Last Theorem, 25 years later Kenneth A. Ribet  129-101 
May 21, 2014  16:00-17:00  Classification of Calabi-Yau threefolds of type K Kenji Hashimoto  129-310 
Dec 17, 2015  15:00-16:00  Random semigroups in solvable linear groups file Keivan Mallahi-Karai  129-104 
Dec 12, 2016  16:00-17:00  On the chromatic number of structured Cayley graphs Keivan Mallahi-Karai  129-301 
Dec 10, 2019  16:30-18:00  Spectral independence of compact groups Keivan Mallahi-Karai  129-406 
Oct 04, 2022  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 
Jun 11, 2014  16:00-17:00  Mirror symmetry and K3 surfaces Kazushi Ueda  129-301 
May 02, 2016  17:00-18:00  Stability of heat kernel estimates under Feynman-Kac perturbations for symmetric Markov processes Kazuhiro Kuwae  27-116 
Mar 19, 2018  11:00-12:10  Twisted Donaldson Invariant (3/19-3/22"room 24-112.25-103) KATO Tsuyoshi  25-103