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
2019-06-10  14:00-16:00  Delta-invariants of complete intersection log del Pezzo surfaces 김인균  129-406 
2018-04-11  15:00-17:00  Analysis of pseudoholomorphic curves and Hofer's displacement energy 오용근  129-406 
2018-04-12  10:00-12:00  Analysis of pseudoholomorphic curves and Hofer's displacement energy 오용근  129-406 
2018-05-15  10:30-12:00  The monodromy map and Darboux coordinates on the SL(2,C)-character variety Chaya Norton  129-406 
2018-05-21  16:00-17:30  Generalized Donaldson-Thomas Invariants via Kirwan Blowups Michail Savvas  129-406 
2019-10-18  11:00-12:00  On a census of right-angled hyperbolic polyhedra file Andrey Vesnin  129-406 
2018-07-03  15:00-17:00  The topological Fukaya category and mirror symmetry for 3d toric LG models Nicolo Sibilla  129-406 
2018-07-04  15:00-17:00  Log schemes, root stacks and parabolic bundles Nicolo Sibilla  129-406 
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2019-12-17  16:00-18:00  Common hyperinvariant subspaces through the generalized spherical Aluthge transforms for commuting pairs of operators Jasang Yoon  129-406 
2019-11-27  16:00-17:00  Quantum group and canonical basis 권재훈  129-406 
2019-12-13  17:00-18:00  Quarernionic projective spaces and 7-sphere 이재혁  129-406 
2018-10-30  16:00-17:30  The mapping class groups of Heegaard splittings Sangbum Cho  129-406 
2020-10-26  16:00-18:00  Asymptotic translation lengths and normal closures of pseudo-Anosov mapping classes 백형렬  129-406 
2018-11-13  17:00-18:00  A/B Testing - why you should do it and why it could be hard 이종호  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 
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 
2021-07-05  14:00-16:00  Algebraic operations on Fukaya category 조철현  129-406