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
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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
2015-12-17  15:00-16:00  Random semigroups in solvable linear groups Keivan Mallahi-Karai  129-104
2016-12-12  16:00-17:00  On the chromatic number of structured Cayley graphs Keivan Mallahi-Karai  129-301
2019-12-10  16:30-18:00  Spectral independence of compact groups Keivan Mallahi-Karai  129-406
2014-06-11  16:00-17:00  Mirror symmetry and K3 surfaces Kazushi Ueda  129-301
2016-05-02  17:00-18:00  Stability of heat kernel estimates under Feynman-Kac perturbations for symmetric Markov processes Kazuhiro Kuwae  27-116
2018-03-19  11:00-12:10  Twisted Donaldson Invariant (3/19-3/22"room 24-112.25-103) KATO Tsuyoshi  25-103
2018-11-28  14:00-15:30  Geometric structures from dynamical rigidity Kathryn Mann  129-301
2016-07-12  16:00-18:00  The Teichmüller diameter of the thick part of moduli space Kasra Rafi  129-301
2016-07-19  16:00-17:00  Global a priori estimates below the natural exponent for quasilinear equations in non-smooth domains Karthik Adimurthi  129-406
2019-12-23  15:00-16:00  Uniform L^{infty}, Lipschitz and C^{1,alpha} estimates for quasilinear parabolic equations Karthik Adimurthi  27-116
2022-07-05  15:00-17:00  Overview of DeGiorgi-Nash-Moser theory Karthik Adimurthi  27-325
2021-09-29  16:00-18:00  Minimal dynamical systems, C*-algebras, and the classification program Karen Strung  선택
2022-07-18  11:00-12:00  New multiplicity results for critical p-Laplacian problems (joint work with Carlo Mercuri) Kanishka Perera  27-220
2021-12-23  16:00-17:00  Weighted estimates for maximal product of spherical averages Kalachand Shuin  선택
2021-12-24  16:00-17:00  Weighted estimates for bilinear Bochner-Riesz means at the critical index Kalachand Shuin  선택
2021-12-24  17:00-18:00  Bilinear Bochner-Riesz means and square function Kalachand Shuin  선택
2022-05-17  16:00-16:30  Bilinear Bochner-Riesz means and square function Kalachand shuin  129-101
2019-04-05  16:00-18:00  Dynamics of continued fractions and conjecture of Mazur-Rubin Jungwon Lee  27-325
2018-12-14  11:00-12:00  Ergodicity and nodal counting of eigenfunctions on 3-manifolds Junehyuk Jung  27-220
2016-06-16  16:00-17:30  Fractals and fractal wavelets Judith Packer  129-301