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
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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.

Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
Subject
Nov 04, 2014  16:00-17:00  A note on the pointwise convergence for the Schrödinger equation 조주희  27-325
Jul 03, 2015  16:00-17:00  Nonlocal p-Laplace equations depending on the Lp norm of the gradient Michel Chipot  27-325
Sep 18, 2015  16:00-17:00  Zeta regularized determinant over Riemann surfaces 박진성  27-325
Apr 10, 2015  11:00-12:00  Stable Matching in Large Economies 김진우  27-325
May 01, 2015  11:00-12:00  심방 세동 현상을 이해하기 위한 수학적 모델의 시뮬레이션과 분석 이영선  27-325
Jan 08, 2016  15:00-16:00  Substitution dynamical systems 손영환  27-325
May 15, 2015  11:00-12:00  Boundary layer for compressible flow Tong Yang  27-325
May 26, 2015  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325
May 27, 2015  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325
May 28, 2015  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325
May 21, 2015  11:00-12:00  Numerical simulations of the primitive equations with humidity and saturations above mountain 홍영준  27-325
Mar 09, 2016  16:00-17:00  Linear parabolic boundary-value problems in generalized Morrey spaces Lubomira G. Softova  27-325
Mar 19, 2016  10:00-11:00  Riesz potential type estimates for parabolic equations with measurable nonlinearities 김유찬  27-325
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? 김현민  27-325
Jun 18, 2016  10:00-13:00  Existence and regularity results of very weak solutions to nonlinear elliptic equations 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