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.
제목
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2015-05-29  09:00-11:00  Regularity for elliptic and parabolic equations Lihe Wang  27-116 
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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  09:00-11:00  An introduction to intrinsic scaling Lecture II Jose Miguel Urbano  27-325 
2019-12-11  09:00-11:00  HYKE Intensive Lectures on Symmetric Hyperbolic Systems of Balance Laws and State file Tommaso Ruggeri / Masaru Sugiyama  27-220 
2021-05-28  09:00-11:00  Nonuniqueness in law for stochastic hypodissipative NSE Marco Rehmeier  27-220 
2021-07-27  09:00-11:00  On the Cauchy problem for quasilinear dispersive PDEs Ⅱ 오성진  선택