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
2015-05-15  11:00-12:00  Boundary layer for compressible flow Tong Yang  27-325
2015-05-26  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325
2015-05-27  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325
2015-05-28  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325
2015-05-21  11:00-12:00  Numerical simulations of the primitive equations with humidity and saturations above mountain 홍영준  27-325
2016-03-09  16:00-17:00  Linear parabolic boundary-value problems in generalized Morrey spaces Lubomira G. Softova  27-325
2016-03-19  10:00-11:00  Riesz potential type estimates for parabolic equations with measurable nonlinearities 김유찬  27-325
2015-06-11  16:00-17:00  Convergence of Eisenstein series on Kac--Moody groups 이규환  27-325
2015-09-30  10:30-12:00  Geometric structures modeled on smooth horospherical varieties of Picard number one 김신영  27-325
2015-11-14  09:00-11:00  What are the nonlinear matrix equations? 김현민  27-325
2016-06-18  10:00-13:00  Existence and regularity results of very weak solutions to nonlinear elliptic equations 유승진  27-325
2016-05-16  16:00-17:00  DYNAMIC CONTACT OF NONLINEAR BEAMS Jeongho Ahn  27-325
2016-06-21  16:00-17:00  An inductive formula of the Gross-Keating invariant of a quadratic form 조성문  27-325
2017-01-05  10:00-12:00  Regularity theory for elliptic equations Lihe Wang  27-325
2017-01-05  16:00-18:00  Regularity theory for parabolic equations Lihe Wang  27-325
2017-03-24  16:00~16:50  Regularity of $$extract_itex$$\omega$$/extract_itex$$-minimizers for a class of functionals with non-standard growth 옥지훈  27-325
2016-10-11  16:00-17:00  Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations 오성진  27-325
2016-10-24  16:00-18:30  Bounded Euler number of actions of 2-orbifold groups on the circle Yoshifumi Matsuda  27-325
2016-10-21  16:00-18:00  Volumes of knots, links and polyhedra in the hyperbolic, spherical and Euclidean spaces Alexander Mednykh  27-325
2017-05-19  16:00-17:00  The p-Laplacian: old and new Pavel Drabek  27-325