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
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2014-03-25  14:00-15:00  Persistent Homology Gunnar E. Carlsson  129-101
2014-03-25  16:00-17:00  Structures on Persistence Barcodes and Generalized Persistence Gunnar E. Carlsson  129-101
2014-08-29  16:00-19:00  Arithmetic Symmetry 김민형  129-101
2015-07-04  15:00-16:00  A survey of alternating permutations Richard P. Stanley  129-101
2015-11-10  16:00-20:00  Pressure metric on the Teichmüller space of surfaces with boundary II Binbin Xu  129-101
2016-07-15  16:00-17:30  Mechanics or Statistics? From Optimization to Natural Language Processing. Problems in Financial Prediction Seunghwan Lee, PhD  129-101
2016-11-17  16:00-17:00  알파고의 바둑 그리고 여자의 바둑 조혜연  129-101
2016-12-08  17:30-18:30  산업계의 변화 동향 및 스타트업의 기회 김이식  129-101
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2017-07-25  15:00-17:00  Derivation of effective equations for interacting many particle system Peter Pickl  129-101
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
2018-05-03  11:00-12:00  Summary of Calabi-Yau Geometry Shing-Tung Yau  129-101
2019-03-27  16:00-17:30  Centralizing centralizers Alexander Guterman  129-101
2021-09-07  16:40-17:10  KNOT CONCORDANCE AND H-COBORDISM 이동수  129-101
2021-10-05  16:00-16:30  Analytic theory of Itô-stochastic differential equations 이해성  129-101
2021-10-19  16:40-17:10  p-adic properties for Taylor coecients of half-integral weight modular forms on Γ_1(4) 김지구  129-101
2019-09-18  16:00-17:00  Fermat's Last Theorem, 25 years later Kenneth A. Ribet  129-101
2020-11-20  15:30-17:45  Zeta함수와 L함수에 대한 역사적 고찰 신석우  129-101