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.
제목
2015-11-02  10:00-12:30, 14:00-18:00  Introduction to deal.II Wolfgang Bangerth  선택
2018-07-10  10:00-12:30  Lectures on quiver Hecke algebras 김명호  129-406
2018-08-13  10:00-12:30  Monte Carlo methods from the perspective of financial engineering 안신미  129-104
2018-08-29  10:00-12:00,14:00-16:00  Optimal transport and martingale optimal transport, and their applications in economics and finance Tongseok Lim  27-325
2016-06-08  10:00-12:00, 13:30-14:30  The flexible Bayesian hierarchical modeling’s and their application in the Analysis of Financial Data Inyoung Kim  129-406
2014-03-17  10:00-12:00  The Effect of Gaussian White Noise on Dynamical Systems Barbara Gentz  129-307
2014-07-07  10:00-12:00  Introduction to Large Deviation Theory I 강완모  27-325
2014-07-09  10:00-12:00  Introduction to Large Deviation Theory II 강완모  27-116
2014-07-11  10:00-12:00  Introduction to Large Deviation Theory III 강완모  27-325
2014-06-13  10:00-12:00  Ideal triangulations, the A-polynomial and beyond Roland van der Veen  129-406
2014-07-29  10:00-12:00  The best hope for the geometric Langlands program Philsang Yoo  129-406
2014-07-29  10:00-12:00  Regularity of Navier-Stokes equations and related equations based on De Giorgi method II Alexis F. Vasseur  27-220
2016-02-19  10:00-12:00  Cluster algebra on the braids 조진석  129-406
2015-07-27  10:00-12:00  Spectral Analysis of Graphs using Quantum Probability Nobuaki Obata  129-104
2015-07-28  10:00-12:00  Spectral Analysis of Graphs using Quantum Probability Nobuaki Obata  129-104
2015-12-04  10:00-12:00  Recent Progress in Numerical Analysis and Image Processing Stanley Osher  27-220
2017-01-05  10:00-12:00  Regularity theory for elliptic equations Lihe Wang  27-325
2017-02-08  10:00-12:00  Lecture 3. The Virasoro Algebra Jethro van Ekeren  129-406
2017-07-26  10:00-12:00  Derivation of effective equations for interacting many particle system Peter Pickl  129-101
2017-07-27  10:00-12:00  Derivation of effective equations for interacting many particle system Peter Pickl  129-101