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

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.
2014-07-02  16:00-17:00  Decoupling Techniques for Coupled PDEs in Multi-physics Applications Mo Mu  선택 
2014-11-04  17:00-18:00  이자율 파생상품의 구조와 그 이해 유석현  선택 
2014-12-09  17:00-18:00  Balanced wall for random groups Piotr Przytycki  선택 
2014-11-07  11:00-12:00  Hybrid Parallelization and GPGPU for Fast Computation of the Radiative Transport Equation Hiroshi Fujiwara  선택 
2014-11-07  10:00-11:00  Stability of the CIP scheme applied to advection equations Yuusuke Iso  선택 
2015-11-30  15:00-16:00  Spectral methods for convection-diffusion problems Jae-Hun Jung  선택 
2015-12-01  15:00-16:00  Pseudospectral methods for hyperbolic equations Jae-Hun Jung  선택 
2015-12-07  14:00-17:00  Nonlinear stochastic games, p-Laplace type equations and applications Mikko Parviainen  선택 
2015-05-07  11:00-12:15  L^1 error estimates for balance laws with space-dependent source Debora Amadori  선택 
2015-05-14  14:00-15:15  Synchronization of finite-state pulse-coupled oscillators 유한백  선택 
2015-05-26  16:00-17:00  Multilevel Monte Carlo Finte Element for Stochastic Optimal Control Problem 심임보  선택 
2015-09-14  16:00-17:30  Parameter-robust preconditioning for systems of partial differential equations 이정훈  선택 
2016-05-11  17:00-18:30  Handle body subgroups in mapping class groups Koji Fujiwara  선택 
2015-10-23  10:30-12:00  function spaces on quantum tori Xiao Xiong  선택 
2015-11-03  14:00-16:00  Introduction to deal.II Wolfgang Bangerth  선택 
2015-11-04  09:30-10:30  Introduction to deal.II Wolfgang Bangerth  선택 
2015-11-05  13:00-17:00  Introduction to deal.II Wolfgang Bangerth  선택 
2015-11-06  10:00-13:00, 15:00-17:00  Introduction to deal.II Wolfgang Bangerth  선택 
2015-11-02  10:00-12:30, 14:00-18:00  Introduction to deal.II Wolfgang Bangerth  선택 
2015-11-13  15:00-16:00  Spectral methods for solving PDEs with singular defect terms Jae-Hun Jung  선택