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
2019-05-15  16:00-18:00  Vector-valued function theory (II) 이우영  129-301
2019-05-14  15:00-17:30  Martin boundary covers Floyd boundary Wenyuan YANG  27-220
2019-05-08  16:00-18:00  Vector-valued function theory (I) 이우영  129-301
2019-05-07  16:30-18:00  Are difficult math problems enough to protect sensitive information? Luis Hernandez  129-301
2019-05-03  16:00-17:00  Infinite rank of abelian varieties over certain infinite extensions Bo-Hae Im  27-325
2019-05-03  16:00-17:00  Systemic Risk Quantification via Shock Amplification in Financial Networks 김경국  129-301
2019-05-01  16:00-17:30  Order unit norms arising from separable multi-qubit X-states 한경훈  129-301
2019-04-26  16:00-17:00  Categorical similarities among the finite dimensional module categories over quantum affine algebras 오세진  27-116
2019-04-24  16:00-17:30  Halmos two projections theorem and some of its applications Qingxiang Xu  129-301
2019-04-24  17:00~18:00  The cohomology class of the Peterson variety Philippe Nadeau  129-406
2019-04-23  13:00-14:00, 15:30-16:30  Dynamical analysis of skew-product models and applications 이정원  27-220
2019-04-23  16:00-17:30  Exceptional collections and toric degenerations of del Pezzo surfaces 조용화  129-301
2019-04-16  16:00-17:00  On the inverse Galois problem with ramification conditions Joachim König  27-325
2019-04-12  16:00-18:00  Classification of strongly positive representations of GU(n,n) and its application Yeonsu Kim  27-325
2019-04-11  14:00-16:00  On motivic cohomology on singular k-schemes 박진현  129-301
2019-04-10  11:00-12:15  Performance and Scalability Analysis of a Coupled Dual Porosity Stokes Model Implemented with FEniCS Craig C. Douglas  선택
2019-04-09  15:00-16:00  A construction of multiplicity class from Hesselink stratification 이철규  129-406
2019-04-05  16:00-18:00  Dynamics of continued fractions and conjecture of Mazur-Rubin Jungwon Lee  27-325
2019-04-04  14:00-16:00  Motivic cohomology on smooth k-schemes 박진현  129-301
2019-04-03  11:00-12:00  Minimizers in generalized Orlicz spaces Arttu Karppinen  27-325