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
2016-05-10  16:00-18:00  AVERAGING OPERATORS ALONG HOLOMORPHIC CURVES file 양찬우  27-116 
2023-11-21  16:00-17:00  The modified scattering for Dirac equations of scattering-critical nonlinearity 양창훈  27-116 
2024-11-15  16:00-17:00  Modified scattering for Dirac equations of scattering-critical nonlinearity 양창훈  129-301 
2023-02-03  15:00-17:00  Infinitely wide neural networks 양홍석  선택 
2023-02-08  15:00-17:00  Infinitely wide neural networks 양홍석  선택 
2023-02-10  15:00-17:00  Infinitely wide neural networks 양홍석  선택 
2024-09-03  14:00-16:00  An extended Vinogradov's mean value theorem 연기석  27-116 
2021-05-26  10:00-11:00  Characterizations of the plane and the catenoid as free boundary minimal surfaces 연응범  27-220 
2022-06-16  13:00-14:30  Quasi-isometric invariants of CAT(0) cube complexes 오상록  129-301 
2015-05-12  16:00-17:00  Global well-posedness of the energy critical Maxwell-Klein-Gordon equation 오성진  129-301 
2016-10-11  16:00-17:00  Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations 오성진  27-325 
2016-11-08  16:00-18:00  Global well-posedness of abelian gauge theories for small critical Sobolev data 오성진  27-116 
2019-05-17  10:00-14:30  An introduction to black holes and the cosmic censorship conjectures I &II 오성진  27-220 
2021-07-26  09:00-12:00  On the Cauchy problem for quasilinear dispersive PDEs Ⅰ 오성진  선택 
2021-07-27  09:00-11:00  On the Cauchy problem for quasilinear dispersive PDEs Ⅱ 오성진  선택 
2021-07-29  09:00-11:00  On the Cauchy problem for quasilinear dispersive PDEs III 오성진  선택 
2021-07-30  09:00-11:00  On the Cauchy problem for quasilinear dispersive PDEs IV 오성진  선택 
2021-11-25  16:00-18:00  A tale of two tails 오성진  선택 
2023-10-31  16:00-18:00  Restriction estimates for quadratic manifolds of arbitrary codimensions 오세욱  27-116 
2022-06-03  17:00-18:00  Maximal and sharp regularity bounds on averages over curves 오세욱  선택