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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Dec 08, 2023  09:00-18:00  2023 Mini Workshop on Nonlinear PDEs from Fluid Mechanics Milton Lopes Filho 외  129-104 
Dec 06, 2019  09:00-17:00  HYKE Intensive Lectures on Symmetric Hyperbolic Systems of Balance Laws and State file Tommaso Ruggeri / Masaru Sugiyama  27-220 
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Jul 26, 2021  09:00-12:00  On the Cauchy problem for quasilinear dispersive PDEs Ⅰ 오성진  선택 
Oct 13, 2023  09:00-12:00  HYKE-Hwarang Intensive Lectures Hayato Chiba  27-325 
May 29, 2015  09:00-11:00  Regularity for elliptic and parabolic equations Lihe Wang  27-116 
Nov 14, 2015  09:00-11:00  What are the nonlinear matrix equations? file 김현민  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  09:00-11:00  An introduction to intrinsic scaling Lecture II Jose Miguel Urbano  27-325 
Dec 11, 2019  09:00-11:00  HYKE Intensive Lectures on Symmetric Hyperbolic Systems of Balance Laws and State file Tommaso Ruggeri / Masaru Sugiyama  27-220 
May 28, 2021  09:00-11:00  Nonuniqueness in law for stochastic hypodissipative NSE Marco Rehmeier  27-220 
Jul 27, 2021  09:00-11:00  On the Cauchy problem for quasilinear dispersive PDEs Ⅱ 오성진  선택