M8200 Direct methods of calculus of variations

Faculty of Science
Spring 2003
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ondřej Došlý, DrSc.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
First, the undirect methods of the Calculus of Variations will be briefly discussed.. The main attention will be devoted to direct methods, i.e. to the construction of a minimizing sequence and to conditions of solvability of variational problems. One of the main aims of the subject is also to show the application the results of the course of functional analysis in solving of variational problems.
Syllabus
  • 1. Classical methods of the Calculus of Variations, Euler-Lagrange equation, first variation, second variation, historical remarks. 2. Sobolev spaces, imbedding, basic properties. 3. Convexity and generalized convexity in variational problems, polyconvex, quasconvex and rank-1 convex functions. 4. Direct methods of solution of vectorial variational problems.
Literature
  • DACOROGNA, Bernard. Direct methods in the calculus of variations. Berlin: Springer-Verlag, 1989, ix, 308. ISBN 0387504915. info
Assessment methods (in Czech)
Ustní zkouška.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2011, Spring 2013, Spring 2015, Spring 2017, Spring 2019.
  • Enrolment Statistics (Spring 2003, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2003/M8200