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
Feb 06, 2017  14:00-15:30  Lecture 2. The Free Fermion and the Boson-Fermion Correspondence Jethro van Ekeren  129-406 
Feb 08, 2017  10:00-12:00  Lecture 3. The Virasoro Algebra Jethro van Ekeren  129-406 
Oct 12, 2021  09:30-11:00  Vertex algebras and chiral homology I Jethro van Ekeren  선택 
Oct 14, 2021  09:30-11:30  Vertex algebras and chiral homology II Jethro van Ekeren  선택 
Dec 26, 2018  11:00-12:00  Families of periodic orbits in the restricted three-body problem and the Cieliebak-Frauenfelder-van Koert invariants Jeungeun Park  27-116 
Jun 04, 2022  10:20-10:50  C 1,α-regularity for nonlinear equations Jihoon Ok  27-325 
Oct 08, 2015  09:30-14:30  Post-quantum cryptography:Multivariate Public Key Cryptography Jintai Ding  129-301 
Apr 16, 2019  16:00-17:00  On the inverse Galois problem with ramification conditions Joachim König  27-325 
Dec 05, 2017  17:00-18:30  Computational Algebraic Geometry and Computer Vision I Joe Kileel  129-301 
Dec 06, 2017  17:00-18:30  Computational Algebraic Geometry and Computer Vision II Joe Kileel  129-406 
Dec 08, 2017  17:00-18:30  Computational Algebraic Geometry and Computer Vision III Joe Kileel  129-104 
Jul 14, 2022  16:00-18:00  Renormalization of Dynamical Systems Jonguk Yang  27-317 
Oct 16, 2018  09:00-11:00  An introduction to intrinsic scaling Lecuture 1 Jose Miguel Urbano  27-325 
Oct 19, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325 
Oct 22, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325 
Oct 23, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325 
Oct 17, 2018  09:00-11:00  An introduction to intrinsic scaling Lecture II Jose Miguel Urbano  27-325 
Jun 16, 2016  16:00-17:30  Fractals and fractal wavelets Judith Packer  129-301 
Jun 17, 2016  16:00-17:00  Projective multiresolution structures for Hilbert modules over unital C*-algebras Judith Packer  129-301 
Dec 14, 2018  11:00-12:00  Ergodicity and nodal counting of eigenfunctions on 3-manifolds Junehyuk Jung  27-220