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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2018-10-16  09:00-11:00  An introduction to intrinsic scaling Lecuture 1 Jose Miguel Urbano  27-325 
2018-10-19  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325 
2018-10-22  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325 
2018-10-23  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325 
2018-10-17  11:00-12:00  Exotic quasi-Fuchsian groups 이계선  27-325 
2017-10-20  16:00-18:30  Dynamics on the surfaces 백형렬  27-325 
2017-11-20  16:00-18:00  Dynamics on the surfaces 백형렬  27-325 
2018-11-16  16:00-18:00  The Laplacian on some round Sierpin´ski carpets and Weyl’s asymptotics for its eigenvalues file Naotaka Kajino  27-325 
2018-11-26  15:00-16:30  Generically smooth components of the Hilbert scheme of curves via ruled surfaces file Hristo Iliev  27-325 
2019-01-30  14:00-16:00  The Calderon-Zygmund type estimate for elliptic equations with minimal regular datum. file Shuang Liang  27-325 
2017-12-18  11:00-13:00  Universal sums of generalized polygonal numbers Ben Kane  27-325 
2019-05-03  16:00-17:00  Infinite rank of abelian varieties over certain infinite extensions Bo-Hae Im  27-325 
2019-05-24  17:00-18:00  p-adic analogue of Riemann-Hilbert correspondence Yong Suk Moon  27-325 
2017-12-29  13:00-17:00  A Series of Invited Talks 김유찬외 3인  27-325 
2019-05-31  16:00-17:00  Combinatorial proofs between some classes of partition functions 손재범  27-325 
2018-01-25  10:00-12:00  Regularity of subelliptic equations Lihe Wang  27-325 
2019-10-02  16:00-18:00  Maximal regularity for local minimizers of non-autonomous functionals 옥지훈  27-325 
2019-10-12  15:00-17:00  Regularity for generalized double phase functionals 오제한  27-325 
2018-07-02  16:00-17:30  Annulus SLE partition functions and martingale-observables 강남규  27-325