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(화)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(수)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(금)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(월)09:00 -11:00 Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

10/23(화)09:00 -11:00 Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
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2019-05-31  15:00-16:00  On $C^{1/2,1}_{t,x}$, $C^{1,2}_{t,x}$, and $C^{0,0}_{t,x}$ estimates for linear parabolic equations in divergence, non-divergence, and double-divergence form 김세익  27-116 
2019-05-31  16:00-17:00  INTERACTION OF FLUID AND RIGID BODY OR PARTICLES, AND APPLICATIONS 배형옥  27-116 
2019-06-14  15:00-17:00  Abundance of irreducible tensor product of linear operators Caixing Gu  27-116 
2019-06-20  15:00-18:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
2019-06-21  10:00-12:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
2019-07-05  14:00-15:30  Effective equidistribution of rational points on expanding horospheres 이민  27-116 
2019-06-19  17:00-18:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
2019-06-20  10:00-12:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
2019-06-21  14:00-16:00  Regularity theory for elliptic and parabolic equations in non-divergence form Lihe Wang  27-116 
2020-07-29  11:00-12:00  Structure analysis of direct sampling method in 3D electromagnetic inverse scattering problem 강상우  27-116 
2019-07-19  16:00-17:00  Diophantine analysis on moduli of local systems Peter Junho Whang  27-116 
2019-07-23  16:00-17:00  Dynamics of the incompressible Euler equations at critical regularity 정인지  27-116 
2019-08-08  16:00-17:00  On the optimal formation of interacting particles -- maximal variance problem and its generalization Tongseok Lim  27-116 
2019-08-12  16:00-17:00  The Strauss conjecture on negatively curved backgrounds Wang, Chengbo  27-116 
2019-09-17  16:00-18:00  Endpoint estimates for the circular maximal function file 이주영  27-116 
2019-09-24  16:00-18:00  Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials file 유재현  27-116 
2019-10-01  16:00-18:00  Maximal estimates for the bilinear spherical average operator file 정은희  27-116 
2019-10-22  16:00-17:00  Well-posedness issues of some dispersive equations under the periodic boundary condition file 곽철광  27-116 
2019-10-22  17:00-18:00  Sharp resolvent estimates for the Lam´e operator and failure of Carleman estimates file 권예현  27-116 
2019-10-28  13:00-15:00  ynamics on PGL_2 over a field over Laurent series 권상훈  27-116 
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