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Introduction to generalised Young measures

Informacje ogólne

Kod przedmiotu: 1000-1M20GYM Kod Erasmus / ISCED: 11.1 / (0541) Matematyka
Nazwa przedmiotu: Introduction to generalised Young measures
Jednostka: Wydział Matematyki, Informatyki i Mechaniki
Grupy: Przedmioty monograficzne dla matematyki 2 stopnia
Seminaria monograficzne dla matematyki 2 stopnia
Punkty ECTS i inne: (brak)
zobacz reguły punktacji
Język prowadzenia: (brak danych)
Rodzaj przedmiotu:


Pełny opis: (tylko po angielsku)

In the study of PDEs, one cannot realistically hope for better compactness

than in the weak topologies, which reasonably describe measurements of

physical quantities. The phenomena that are less understood do not usually

lead to linear equations, making the interaction between nonlinear

quantities and weakly convergent sequences an ubiquitous theme in the study

of nonlinear PDEs. In this course, we will learn about generalized Young

measures, which are especially useful tools to describe the effective

limits of nonlinearities applied to weakly convergent sequences in Lebesgue

spaces. In particular, these objects efficiently keep track of

concentration and oscillation effects, which are the main obstructions to

strong convergence. Thus, Young measures are naturally used in many

branches of PDE theory, of which we will focus on their role in the

Calculus of Variations, where the notion first emerged from the ideas of

L.C. Young. We will thoroughly explore the functional analytic and measure

theoretic realities of generalized Young measures, with a focus on

identifying oscillation and concentration effects, or lack thereof. We will

use this basic understanding to study weak sequential continuity and lower

semi-continuity of energy functionals on linear PDE constrained subsets of

Lebesgue spaces. Such problems arise in elasticity, plasticity, composites,

fluids, and electromagnetism, to name a few; more abstract applications

arise in differential geometry and geometric measure theory.

Przedmiot nie jest oferowany w żadnym z aktualnych cykli dydaktycznych.
Opisy przedmiotów w USOS i USOSweb są chronione prawem autorskim.
Właścicielem praw autorskich jest Uniwersytet Warszawski.