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
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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.

Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
Subject
Oct 10, 2018  16:30-17:30  Fundamental concepts in option pricing: Comparison of binomial tree model, partial differential equation approach, and the martingale method 최건호  27-325
Oct 16, 2018  09:00-11:00  An introduction to intrinsic scaling Lecuture 1 Jose Miguel Urbano  27-325
Oct 19, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325
Oct 22, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325
Oct 23, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325
Oct 17, 2018  11:00-12:00  Exotic quasi-Fuchsian groups 이계선  27-325
Oct 20, 2017  16:00-18:30  Dynamics on the surfaces 백형렬  27-325
Nov 20, 2017  16:00-18:00  Dynamics on the surfaces 백형렬  27-325
Nov 16, 2018  16:00-18:00  The Laplacian on some round Sierpin´ski carpets and Weyl’s asymptotics for its eigenvalues Naotaka Kajino  27-325
Nov 26, 2018  15:00-16:30  Generically smooth components of the Hilbert scheme of curves via ruled surfaces Hristo Iliev  27-325
Jan 30, 2019  14:00-16:00  The Calderon-Zygmund type estimate for elliptic equations with minimal regular datum. Shuang Liang  27-325
Dec 18, 2017  11:00-13:00  Universal sums of generalized polygonal numbers Ben Kane  27-325
May 03, 2019  16:00-17:00  Infinite rank of abelian varieties over certain infinite extensions Bo-Hae Im  27-325
May 24, 2019  17:00-18:00  p-adic analogue of Riemann-Hilbert correspondence Yong Suk Moon  27-325
Dec 29, 2017  13:00-17:00  A Series of Invited Talks 김유찬외 3인  27-325
May 31, 2019  16:00-17:00  Combinatorial proofs between some classes of partition functions 손재범  27-325
Jan 25, 2018  10:00-12:00  Regularity of subelliptic equations Lihe Wang  27-325
Oct 02, 2019  16:00-18:00  Maximal regularity for local minimizers of non-autonomous functionals 옥지훈  27-325
Oct 12, 2019  15:00-17:00  Regularity for generalized double phase functionals 오제한  27-325
Jul 02, 2018  16:00-17:30  Annulus SLE partition functions and martingale-observables 강남규  27-325