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
2022-12-22  14:00-16:00  Fully nonlinear parabolic equations Lihe Wang  27-325 
2021-11-05  10:00-12:00  Regularity of elliptic partial differential equations 1 Lihe Wang  선택 
2021-11-12  10:00-12:00  Analysis for Elliptic Equations 2 Lihe Wang  선택 
2021-11-19  10:00-12:00  Analysis for Elliptic Equations #3 Lihe Wang  선택 
2021-12-03  10:00-12:00  Analysis for Elliptic Equations #4 Lihe Wang  선택 
2019-01-23  16:00-17:00  Regularity for elliptic equations in heterogeneous media Li-Ming Yeh  129-301 
2014-04-07  14:00-15:00  Dfferential Games of Evasion and Pontryagin\'s Lemma Lev Yugay  129-307 
2017-04-27  13:00-15:00  Information Asymmetry in Mathematical Finance Lee, Kiseop  129-104 
2021-12-20  16:00-17:00  The Navier-Stokes-wall-grafted polymer system, global well-posedness, and polymer drag reduction LA, Joonhyun  선택 
2022-08-24  16:30-17:00  Heat kernel estimates for a large class of anisotropic Markov process Kyung-Youn Kim  129-301 
2015-08-10  16:00-17:00  Nonlinear noise excitation, Intermittency and Multifractality Kunwoo Kim  27-116 
2016-05-11  17:00-18:30  Handle body subgroups in mapping class groups Koji Fujiwara  선택 
2021-03-16  11:00-12:00  Transfer operators and limit laws for typical cocycles Kiho Park  선택 
2022-05-06  16:00-18:00  On an upper bound of the average analytic rank of a family of elliptic curves Keunyoung Jeong  27-325 
2019-09-18  16:00-17:00  Fermat's Last Theorem, 25 years later Kenneth A. Ribet  129-101 
2014-05-21  16:00-17:00  Classification of Calabi-Yau threefolds of type K Kenji Hashimoto  129-310 
2015-12-17  15:00-16:00  Random semigroups in solvable linear groups file Keivan Mallahi-Karai  129-104 
2016-12-12  16:00-17:00  On the chromatic number of structured Cayley graphs Keivan Mallahi-Karai  129-301 
2019-12-10  16:30-18:00  Spectral independence of compact groups Keivan Mallahi-Karai  129-406 
2022-10-04  16:00-17:00  On an extreme value law for the unipotent flow on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Keivan Mallahi Karai  선택