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.
Subject
Dec 05, 2024  19:00~21:00  Maximal estimates for various averaging operators and their generalizations Shuijiang Zhao  27-325 
Nov 21, 2024  19:00~21:00  Maximal estimates for various averaging operators and their generalizations Shuijiang Zhao  27-325 
Nov 18, 2024  11:00-13:00  Local superconformal algebras Surya Raghavendran  129-406 
Nov 18, 2024  14:00-16:30  Lagrangian knot problems in symplectic four-manifolds new 김준태  129-309 
Nov 15, 2024  17:00-19:00  Sharp Lp-Lq estimates for the spherical harmonic projection 권예현  27-116 
Nov 15, 2024  10:00-12:00  First-order differential calculi and Laplacians on $q$-deformations of compact semisimple Lie groups 이헌  129-301 
Nov 15, 2024  16:00-17:00  Modified scattering for Dirac equations of scattering-critical nonlinearity 양창훈  129-301 
Nov 15, 2024  14:00-16:30  Lagrangian knot problems in symplectic four-manifolds new 김준태  129-309 
Nov 14, 2024  16:00-16:30  What a colorful world: a biased personal introduction to discrete geometry 이승훈  129-101 
Nov 14, 2024  16:40-17:10  Signed Graph Theory: Extensions and Applications 허철원  129-101 
Nov 12, 2024  17:00-18:00  Recent advances on the weight part of Serre's conjecture new Heejong Lee  선택 
Nov 07, 2024  19:00~21:00  Maximal estimates for various averaging operators and their generalizations Shuijiang Zhao  27-325 
Nov 06, 2024  15:00-16:00  3D mirror symmetry Naichung Conan Leung  129-406 
Nov 06, 2024  16:00-17:00  3d mirror symmetry is mirror symmetry Naichung Conan Leung  129-406 
Nov 05, 2024  16:00-17:00  On the concentration phenomenon for the Sobolev flow Masashi Misawa  27-325 
Nov 05, 2024  10:00-11:00  On the concentration phenomenon for the Sobolev flow Masashi Misawa  27-116 
Nov 05, 2024  16:00-17:00  On the distribution of primitive lattice points in large dimensions 한지영  129-309 
Nov 04, 2024  17:00-18:00  A unified approach to Rohrlich-type divisor sums Toshiki Matsusaka  27-325 
Nov 01, 2024  17:00-18:30  Bases of Norm Generators and Applications 윤종흔  27-116 
Oct 30, 2024  15:00-17:30  De Giorgi's minimizing movements, optimal transport, and bilevel optimization 권도현  27-220