Selected Topics in Analysis: Calculus of Variations
- Lectures
-
MWF 1:00am-1:50am (MTH 0104)
- Instructor
- Georg Dolzmann (
dolzmann@math.umd.edu)
- Office: MATH 3309 (405-5144)
- Office hours: by appointment
- Class web page
-
http://www.math.umd.edu/~dolzmann/Math648C/math648c.html
- Topics
-
This course is an introduction into the calculus of variations, one of the oldest and yet very active fields in mathematics. In the first part of the term we will cover classical aspects which are frequently referred to as indirect methods, in the second part we will discuss the direct methods in the calculus of variations. Possible topics include: Euler-Lagrange equations, Noether's theorem, field theories, existence and regularity of minimizers, lower semicontinuity, notions of convexity, Young measures, homogenization, gamma convergence. Some of these topics might be covered during the Spring Term.
- Text
- M. Giaquinta and S. Hildebrandt,
Calculus of variations,
Grundlehren der mathematischen Wissenschaften, Volumes 310 and 311, Springer, 1996
C. M. Morrey,
Multiple integrals in the calculus of variations,
Grundlehren der mathematischen Wissenschaften, Volume 130,
Springer, 1966
M. Giaquinta,
Multiple integrals in the calculus of variations and nonlinear elliptic systems,
Annals of Mathematics Studies, 105,
Princeton University Press, 1983
B. Dacorogna,
Direct methods in the calculus of variations,
Applied Mathematical Sciences, 78.
Springer, 1989
S. Müller,
Variational models for microstructure and phase transitions,
Lecture Notes 2, Max Planck Institute for Mathematics in the Sciences, 1998
- Prerequisites
- A solid knowledge of multi-variable calculus. Fundamental concepts from functional
analysis will be revied in the course.
- Homework
- Several homework sets will be assigned during the course.
- Grading
- Based on homework.
Georg Dolzmann
Last modified: Fri Aug 26 08:06:53 EDT 2005