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.
제목
2019-01-23  16:00-17:00  Regularity for elliptic equations in heterogeneous media Li-Ming Yeh  129-301 
2019-01-23  15:00-16:00  Nitsche-eXtended finite element methods for optimal control problems of elliptic interface equations Xiaoping Xie  129-301 
2019-01-18  14:00-16:00  Macdonald Polynomials: Representation Theory and Combinatorics Cristian Lenart  129-301 
2019-01-16  14:00-16:00  Macdonald Polynomials: Representation Theory and Combinatorics Cristian Lenart  129-406 
2019-01-14  14:00-16:00  Macdonald Polynomials: Representation Theory and Combinatorics Cristian Lenart  129-406 
2019-01-04  16:30-17:30  Birational geometry of moduli spaces of curves: a half-century of questions, conjectures and answers Prof. Ian Morrison  129-301 
2019-01-04  14:00-15:00  "Can you play a fair game of craps with a loaded pair of dice?'' and related problems about factorization in $mathbbR^ge0 [x]$ Prof. Ian Morrison  129-301 
2019-01-03  10:00-11:30  Families of periodic orbits in the restricted three-body problem and the Cieliebak-Frauenfelder-van Koert invariants 김성찬  129-104 
2018-12-26  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 
2018-12-19  11:00-13:00  Wakimoto representations and Parabolic inductions for W-algebras Naoki Genra  27-325 
2018-12-14  11:00-12:00  Ergodicity and nodal counting of eigenfunctions on 3-manifolds Junehyuk Jung  27-220 
2018-12-13  14:00-15:30  Cheeger-Gromov L^2 rho-invariant of 3-manifolds Geunho Lim  129-301 
2018-12-07  15:00-17:00  Discrete radial absorbing boundary condition for wave equations 전영목  129-310 
2018-12-05  16:00-18:00  A canonical decomposition of strong L^2-functions 이우영  129-301 
2018-12-03  14:00-15:00  Log BPS numbers of log Calabi-Yau surfaces 최진원  129-406 
2018-12-03  16:00-18:00  Ring structure of wrapped Floer homology of real Lagrangians in Brieskorn Milnor fibers 배한울  129-406 
2018-11-30  12:00-13:00  Optimal investment and consumption with liquid and illiquid assets 최진혁  129-301 
2018-11-28  16:00-18:00  Quantum information and random matrices Motohisa Fukuda  129-301 
2018-11-28  17:00-18:30  An efficient approach for removing look-ahead bias in the least square Monte Carlo algorithm: Leave-one-out 최재혁  27-325 
2018-11-28  14:00-15:30  Geometric structures from dynamical rigidity Kathryn Mann  129-301