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
$$extract_itex$$6,7,17$$/extract_itex$$

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
2015-10-16  13:30-15:30  Quantum Information Theory Basics 지동표  129-301
2015-10-13  16:00-17:00  Some construction of K3 surfaces motivated by diophantine geometry 김도형  129-301
2015-03-03  16:00-18:30  Introduction to Cluster Algebras coming from surfaces I, II 이경용  129-301
2015-03-04  16:00-17:00  Cluster algebras and mirror symmetry 이경용  129-301
2015-10-20  15:00-17:00  Quantum Information THeory Basics 1 지동표  129-301
2015-10-23  13:00-15:00  Quantum Information THeory Basics 1 지동표  129-301
2015-03-13  10:30-12:00  Weighted Fourier algebra on compact Lie groups and the dimensional information 이훈희  129-301
2015-04-01  16:00-18:00  Group actions and Frobenius manifolds 이병호  129-301
2015-04-02  16:00-18:00  Group actions and Frobenius manifolds 이병호  129-301
2015-11-05  15:00-17:00  Free Energy of Spherical Spin Glass Model 이지운  129-301
2015-03-27  10:30-12:00  Projection lifting from the corona algebra using UCT(Universal Coefficients Theorem) 이현호  129-301
2015-11-06  13:30-15:30  Quantum Information Theory Basics 지동표  129-301
2015-11-13  13:30-15:30  Quantum Information Theory Basics 지동표  129-301
2015-11-20  13:30-15:30  Quantum Information Theory Basics 지동표  129-301
2015-03-31  16:00-17:00  A perturbation argument arising in optimal transportation Maria del Mar Gonzalez Nogueras  129-301
2015-04-08  16:30-17:30  Cuspidal curves on Rational Homology Planes Sagar Kolte  129-301
2015-11-27  13:30-15:30  Quantum Information Theory Basics 지동표  129-301
2015-12-04  13:30-15:30  Quantum Information Theory Basics 지동표  129-301
2015-12-14  14:00-17:00  The flatness and Schur product of mono-weakly hyponormal two variable weighted shifts Jasang Yoon  129-301
2015-04-10  15:00-16:00  Geometry of Homotopy Probability Theory 박재석  129-301