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
Jan 05, 2017  10:00-12:00  Regularity theory for elliptic equations Lihe Wang  27-325 
Jan 05, 2017  16:00-18:00  Regularity theory for parabolic equations Lihe Wang  27-325 
Mar 24, 2017  17:00-17:50  Weighted $L^q$ estimates for nonlinear elliptic equations 유승진  27-325 
Mar 24, 2017  16:00~16:50  Regularity of $\omega$-minimizers for a class of functionals with non-standard growth 옥지훈  27-325 
May 19, 2017  16:00-17:00  The p-Laplacian: old and new Pavel Drabek  27-325 
Jun 06, 2017  16:00-17:00  Mathematical and numerical approaches to dynamic contact of nonlinear springs Jeongho Ahn  27-325 
Jun 16, 2017  14:00-16:30  An Introduction to algebra and representation theory in Sage Travis Scrimshaw  27-325 
Jul 06, 2017  16:00-17:00  Generalized Sato-Tate conjecture and weight multiplicities of symplectic Lie algebras 이규환  27-325 
Aug 07, 2017  16:00-18:00  Mirror of Atiyah flop in symplectic geometry Hansol Hong  27-325 
Aug 16, 2017  10:00-11:00  The Vlasov-Poisson-Boltzmann System for the Whole Range of Cutoff Soft Potentials Qinghua Xiao  27-325 
Aug 29, 2017  15:00-16:00  MOD p LOCAL-GLOBAL COMPATIBILITY FOR GLn(Qp) IN THE ORDINARY CASE 박철  27-325 
Aug 29, 2017  16:00-17:00  Statistics of high-dimensional lattices 김승기  27-325 
Oct 20, 2017  16:00-18:30  Dynamics on the surfaces 백형렬  27-325 
Nov 20, 2017  16:00-18:00  Dynamics on the surfaces 백형렬  27-325 
Dec 18, 2017  11:00-13:00  Universal sums of generalized polygonal numbers Ben Kane  27-325 
Dec 29, 2017  13:00-17:00  A Series of Invited Talks 김유찬외 3인  27-325 
Jan 25, 2018  10:00-12:00  Regularity of subelliptic equations Lihe Wang  27-325 
Feb 02, 2018  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  27-325 
Mar 07, 2018  14:00-15:00  Nonlinear Dirichlet problems: old and new file Lucio Boccardo  27-325 
Mar 09, 2018  16:00-17:00  Regularizing effect of the lower order terms in some nonlinear Dirichlet problems file Lucio Boccardo  27-325