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
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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
2018-10-16  16:30-18:00  A decoupling estimate related to Lindelöf hypothesis. 이정진  27-116
2018-10-16  15:00-16:30  UNIFORM SOBOLEV INEQUALITY ON THE d-TORUS 정은희  27-116
2018-10-17  11:00-12:00  Exotic quasi-Fuchsian groups 이계선  27-325
2018-10-17  16:00-18:00  Spectra of weighted Fourier algebras on Lie groups II 이훈희  129-301
2018-10-17  09:00-11:00  An introduction to intrinsic scaling Lecture II Jose Miguel Urbano  27-325
2018-10-19  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325
2018-10-22  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325
2018-10-23  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325
2018-10-23  14:00-16:00  On virtual embeddability between the mapping class groups of some surfaces Takuya KATAYAMA  129-406
2018-10-23  17:00-18:00  Consumption and Portfolio Selection with Necessities and Luxuries 신용현  129-310
2018-10-24  16:00-17:00  Gaussian quantum technologies: teleportation and beyond Gerardo Adesso  129-301
2018-10-25  17:00-18:00  Gaussian quantum technologies: teleportation and beyond Gerardo Adesso  129-301
2018-10-25  11:00-13:00  Introduction to SYZ mirror symmetry 2 Yat-Hin Suen  25-103
2018-10-26  10:00-11:00  Gaussian quantum technologies: teleportation and beyond Gerardo Adesso  129-301
2018-10-27  10:00-11:00  Gaussian quantum technologies: teleportation and beyond Gerardo Adesso  129-104
2018-10-29  10:30-12:00  An introduction to Baker’s theory of linear forms in logarithms Yann Bugeaud  27-325
2018-10-30  16:30-18:00  Continuum limit for discrete nonlinear Schrödinger equations 홍영훈  27-116
2018-10-30  16:00-17:30  The mapping class groups of Heegaard splittings Sangbum Cho  129-406
2018-10-30  15:00-16:00  The linear and nonlinear wave equations with critical Lorentz regularity Javier Ramos  27-116
2018-10-31  16:00-18:00  Geometry of Banach space and norm attaining functions 김선광  129-301