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
$$extract_itex$$14$$/extract_itex$$ , with complements and extensions from a variety of sources (listed in the references), mainly
$$extract_itex$$6,7,17$$/extract_itex$$

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
2021-12-16  16:00-18:00  A brief introduction to differential graded Lie algebras I, II 조창연  129-301
2021-12-14  16:00-18:00  A brief introduction to differential graded Lie algebras I, II 조창연  129-301
2021-12-07  15:00-18:00  The canonical commutation relations and the local geometry of symplectic spaces 김현문  27-325
2021-12-03  10:00-12:00  Analysis for Elliptic Equations #4 Lihe Wang  선택
2021-12-01  15:30-18:00  Asymptotic behavior at singularities of mean curvature flow 최경수  선택
2021-12-01  16:00-17:00  Optimal gradient estimates for elliptic equations with nonstandard growth conditions 임민규  27-220
2021-11-30  16:00-18:00  Cauchy problems for nonlinear wave equations with low regularity data 홍석창  27-220
2021-11-26  14:00-14:30  On Barbalat’s lemma and its applications to collective 저우타오  27-220
2021-11-26  14:30-15:30  On the emergent behaviors of relativistic Cucker-Smale flocks 안현진  27-220
2021-11-26  13:30-14:00  Emergent behaviors of Lohe hermitian sphere particles under time-delayed interactions 황규영  27-220
2021-11-26  16:00-18:00  Magic Pentagram Problem is in QNC^0 but not in NC^0 이수준  선택
2021-11-25  16:00-18:00  A tale of two tails 오성진  선택
2021-11-25  13:30-15:00  Exotic families of Weinstein manifolds with Milnor fibers of ADE types 이상진  27-220
2021-11-24  16:00-18:00  Matrix-valued maximal Calder'on-Zygmund operators and applications Bang Xu  선택
2021-11-19  10:00-12:00  Analysis for Elliptic Equations #3 Lihe Wang  선택
2021-11-19  14:00-16:00  인공지능에 대한 다양한 위협과 안전한 활용 방안 박새롬  선택
2021-11-17  16:00-18:00  Gaussian states and channels over general quantum kinematical systems 박상준  선택
2021-11-16  16:00-16:30  Crystal base and unipotent quantum coordinate ring 장일승  129-101
2021-11-16  16:40-17:10  Quasisymmetric functions and weak Bruhat interval modules of the 0-Hecke algebras 김영훈  129-101
2021-11-16  14:00-15:00  Approximation Methods of Multivariate Functions for Homomorphic Data Ordering 홍승완  129-301