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
Jun 04, 2022  09:40-10:10  Regularity results for the nonlinear thin obstacle problem with double phase in the borderline case Jehan Oh  27-325 
Jul 05, 2016  09:30-15:30  Worst-case to Average-case Reductions for Lattice Problems Phong Nguyen  129-301 
Oct 08, 2015  09:30-14:30  Post-quantum cryptography:Multivariate Public Key Cryptography Jintai Ding  129-301 
Oct 22, 2020  09:30-12:30  Hausdorff dimensions of perturbations of conformal iterated function systerm via thermodynamic formailism 김우연  129-301 
Aug 05, 2020  09:30-11:30  Embedding Carnot groups into bounded dimensional Euclidean spaces with optimal distortion 유상우  27-116 
Aug 07, 2020  09:30-11:30  Embedding Carnot groups into bounded dimensional Euclidean spaces with optimal distortion 유상우  27-116 
Oct 14, 2021  09:30-11:30  Vertex algebras and chiral homology II Jethro van Ekeren  선택 
Apr 06, 2015  09:30-11:00, 14:00-15:30  The Minicourse of lattice algorithm Damien Stehlé  129-406 
Apr 07, 2015  09:30-11:00, 14:00-15:30  The Minicourse of lattice algorithm Damien Stehlé  129-406 
Apr 08, 2015  09:30-11:00, 14:00-15:30  The Minicourse of lattice algorithm Damien Stehlé  129-406 
Apr 09, 2015  09:30-11:00, 14:00-15:30  The Minicourse of lattice algorithm Damien Stehlé  129-406 
Apr 10, 2015  09:30-11:00, 14:00-15:30  The Minicourse of lattice algorithm Damien Stehlé  129-406 
Apr 11, 2015  09:30-11:00, 14:00-15:30  The Minicourse of lattice algorithm Damien Stehlé  129-406 
May 17, 2017  09:30-11:00  Extreme Value Theory in Dynamical Systems Maxim Kirsebom  27-116 
Oct 12, 2021  09:30-11:00  Vertex algebras and chiral homology I Jethro van Ekeren  선택 
May 20, 2022  09:30-11:00  Introduction to the National Institute for Mathematical Sciences and the Future of Industrial Mathematics 김현민  27-116 
Mar 20, 2023  09:30-11:00  Homogeneous dynamics and Laplace eigenfunctions I, II, III 권상훈  129-301 
Mar 13, 2023  09:30-11:00  Homogeneous dynamics and Laplace eigenfunctions I, II, III 권상훈  129-301 
Mar 06, 2023  09:30-11:00  Homogeneous dynamics and Laplace eigenfunctions I, II, III 권상훈  129-301 
Jun 23, 2023  09:30-11:00  Ergodicity of Iwasawa Continued Fractions and Markable Hyperbolic Geodesics II 박성재  129-309