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
2023-02-21  10:30-12:00  An introduction to geometric representation theory and 3d mirror symmetry Justin Hilburn  129-104 
2023-02-23  10:30-12:00  An introduction to geometric representation theory and 3d mirror symmetry Justin Hilburn  129-104 
2023-02-28  10:30-12:00  An introduction to geometric representation theory and 3d mirror symmetry Justin Hilburn  129-104 
2023-04-21  10:30-12:00  Non-freeness of certain two-parabolic groups 김상현  129-309 
2024-01-24  10:30-12:00  Transference theorems, parametric geometry of numbers, and spectra I Yann Bugeaud  27-220 
2024-08-22  10:30-12:00  Outer symplectic billiard Peter Albers  129-406 
2024-10-02  10:30-12:00  Optimal Control for ODEs and PDEs: The Turnpike Phenomenon Michael Schuster  27-325 
2016-04-21  10:30-12:30  Stability of pencils of quadrics and nets of quadrics 변상호  129-301 
2017-01-31  10:30-12:30  Hodge theory 이상욱  129-301 
2021-06-03  10:30-12:30  Locking-free and locally-conservative enriched Galerkin methods for linear poroelasticity 이상현  129-310 
2022-01-27  10:30-12:30  Simultaneous determination of shape and refractive index of a deformed microjet cavity from its resonances 문송기  선택 
2022-08-30  10:30-12:30  Quantitative nonembeddability of nilpotent Lie groups and groups of polynomial growth into superreflexive spaces 유승연  129-301 
2024-07-16  10:30-12:30  Highest weight categories and quasi-hereditary algebras 고한경  129-301 
2021-09-30  10:30-12:40  Schur-Weyl duality, old and new & Quantum symmetric pairs and Schur-type dualities Chun-Ju Lai  선택 
2022-07-11  10:30-13:00  Survival kit on plane curve singularities I Pablo Portilla cuadrado  129-406 
2022-07-19  10:30-13:00  A quadratic form associated with pseudo-periodic homeomorphisms arising from singularity theory. Pablo Portilla cuadrado  129-406 
2022-07-12  10:30-13:00  Survival kit on plane curve singularities II Pablo Portilla Cuadrado  129-406 
2022-07-18  10:30-13:00  Characterizing the geometric monodromy group of an isolated plane curve singularity Pablo Portilla cuadrado  129-406 
2023-12-13  10:30-13:00  Navier-Stokes equations on Riemannian manifolds Maryam Samavaki  129-301 
2024-07-18  10:30-13:00  Highest weight categories and quasi-hereditary algebras 고한경  129-301