Calculus of Variations and Geometric Measure Theory

Two lectures

Boris Mordukhovich , Nina Uraltseva

created by magnani on 27 Apr 2006

4 may 2006


On Thursday, 4 May

In ``Aula Magna'' of the Mathematics Department

I) At 16:00. Boris Mordukhovich,

(Department of Mathematics, Wayne State University) will give a lecture on

``Methods of variational analysis in optimization and control''

II) At 17:30. N.N. Uraltseva

(St. Petersburg State University) will give a lecture on

``Two-phase obstacle problem''

ABSTRACT I. Variational analysis has been recognized as a rapidly growing and fruitful area in mathematics concerning mainly the study of optimization and equilibrium problems, while also applying perturbation ideas and variational principles to a broad class of problems and situations that may be not of a variational nature. It can be viewed as a modern outgrowth of the classical calculus of variations, optimal control theory, and mathematical programming with the focus on perturbationapproximation techniques, sensitivity issues, and applications. One of the most characteristic features of modern variational analysis is the intrinsic presence of nonsmoothness, which naturally enters not only through initial data of optimization-related problems but largely via variational principles and perturbation techniques applied to problems with even smooth data. This requires developing new forms of analysis that involve generalized differentiation.

In this talk we discuss some new trends and developments in variational analysis and its applications mostly based on the author��� recent 2-volume book ���ariational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications,���Springer, 2006. Applications particularly concern optimization and equilibrium problems, optimal control of ODEs and PDEs, mechanics, and economics. The talk does not require preliminary knowledge on the subject.

ABSTRACT II. The regularity of the free boundary in the obstacle-like problem in the presence of two phases will be proved.