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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2017-09-20  15:00-17:00  Structure of Entropy solutions in one space dimension for convex flux and its applications Adimurthi  27-116
2017-09-25  10:00-12:00  Structure of Entropy solutions in one space dimension for convex flux and its applications Adimurthi  27-116
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2017-04-17  16:00-17:30  Some symplectic properties of hypersurface cusp singularities. Lec 1 Ailsa Keating  129-406
2017-04-18  14:00-15:30  Some symplectic properties of hypersurface cusp singularities. Lec 2 Ailsa Keating  129-301
2017-04-19  14:00-15:30  Some symplectic properties of hypersurface cusp singularities. Lec 3 Ailsa Keating  129-406
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2017-07-03  14:00-15:00  Higher dimensional Steinhaus problems Alan Haynes  129-301
2015-09-02  15:00-17:00  What is Weak KAM Theory? / Regularity of solutions of Hamilton-Jacobi equation on a domain Albert Fathi  27-220
2014-11-13  14:00-15:00  Random groups surface subgroups Alden Walker  129-104
2014-09-30  17:00-18:00  Deviation estimates for random walks and acylindrically hyperbolic groups Alessandro Sisto  129-301
2021-03-08  16:30-17:30  On class groups of random number fields Alex Bartel  선택
2021-03-15  16:30-17:30  On class groups of random number fields Alex Bartel  선택
2021-03-22  16:30-17:30  On class groups of random number fields Alex Bartel  선택
2019-03-27  16:00-17:30  Centralizing centralizers Alexander Guterman  129-101
2016-10-21  16:00-18:00  Volumes of knots, links and polyhedra in the hyperbolic, spherical and Euclidean spaces Alexander Mednykh  27-325
2019-01-31  11:00-12:00  Non - Euclidean versions of some classical theorems in the low-dimensional geometry Alexander Mednykh  129-301