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 11, 2015  16:00-17:00  Convergence of Eisenstein series on Kac--Moody groups 이규환  27-325 
Sep 30, 2015  10:30-12:00  Geometric structures modeled on smooth horospherical varieties of Picard number one 김신영  27-325 
Nov 14, 2015  09:00-11:00  What are the nonlinear matrix equations? file 김현민  27-325 
Jun 18, 2016  10:00-13:00  Existence and regularity results of very weak solutions to nonlinear elliptic equations file 유승진  27-325 
May 16, 2016  16:00-17:00  DYNAMIC CONTACT OF NONLINEAR BEAMS Jeongho Ahn  27-325 
Jun 21, 2016  16:00-17:00  An inductive formula of the Gross-Keating invariant of a quadratic form 조성문  27-325 
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  16:00~16:50  Regularity of $\omega$-minimizers for a class of functionals with non-standard growth 옥지훈  27-325 
Oct 11, 2016  16:00-17:00  Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations 오성진  27-325 
Oct 24, 2016  16:00-18:30  Bounded Euler number of actions of 2-orbifold groups on the circle Yoshifumi Matsuda  27-325 
Oct 21, 2016  16:00-18:00  Volumes of knots, links and polyhedra in the hyperbolic, spherical and Euclidean spaces Alexander Mednykh  27-325 
May 19, 2017  16:00-17:00  The p-Laplacian: old and new Pavel Drabek  27-325 
Dec 14, 2016  16:00-17:00  SOBOLEV CAPACITIES IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Nguyen Cong Phuc  27-325 
Mar 24, 2017  17:00-17:50  Weighted $L^q$ estimates for nonlinear elliptic equations 유승진  27-325 
Jul 06, 2017  16:00-17:00  Generalized Sato-Tate conjecture and weight multiplicities of symplectic Lie algebras 이규환  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  16:00-17:00  Statistics of high-dimensional lattices 김승기  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