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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2016-04-21  10:30-12:30  Stability of pencils of quadrics and nets of quadrics 변상호  129-301 
2017-01-31  10:30-12:30  Hodge theory 이상욱  129-301 
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2017-12-04  10:45-12:15  해석학특강 학기말 조별 발표   27-220 
2017-12-06  10:45-12:15  해석학특강 학기말 조별 발표   27-220 
2017-05-18  10:55-11:55  A Multivariate extreme value law (EVL) for maximal geodesic windings around distinct cusps Maxim Kirsebom  129-406 
2022-06-04  11:00-11:30  Global Sobolev regularity for general type of elliptic equations with measure data Pilsoo Shin  27-325 
2014-11-28  11:00-11:50  Stochastic modeling of biochemical networks Hye-Won Kang  129-104 
2018-08-14  11:00-11:50  On high-order methods for moment-closure approximations of kinetic Boltzmann equations James Rossmanith  27-220 
2015-01-20  11:00-12:00  Determinant formula for K-theory of Grassmannians III Tomoo Matsumura  129-301 
2015-05-15  11:00-12:00  Boundary layer for compressible flow Tong Yang  27-325