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

10/16()09:00 11:00 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.

10/17()09:00- 11:00 Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

10/19()09:00 -11:00 Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

10/22()09:00 -11:00 Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

10/23()09:00 -11:00 Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
Subject
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Oct 24, 2016  16:00-18:30  Bounded Euler number of actions of 2-orbifold groups on the circle Yoshifumi Matsuda  27-325 
Oct 21, 2016  16:00-18:00  Volumes of knots, links and polyhedra in the hyperbolic, spherical and Euclidean spaces Alexander Mednykh  27-325 
May 19, 2017  16:00-17:00  The p-Laplacian: old and new Pavel Drabek  27-325 
Dec 14, 2016  16:00-17:00  SOBOLEV CAPACITIES IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS Nguyen Cong Phuc  27-325 
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Jun 16, 2017  14:00-16:30  An Introduction to algebra and representation theory in Sage Travis Scrimshaw  27-325 
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Aug 07, 2017  16:00-18:00  Mirror of Atiyah flop in symplectic geometry Hansol Hong  27-325 
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May 29, 2018  09:00-10:00  Backward SDEs and their applications to stochastic optimization and SPDE 남기훈  27-325 
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Jul 27, 2018  15:00-17:00  Regularity for multi-phase variational problems 오제한  27-325