Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Variational Calculus I - NDIR060

Title:	Variační počet I
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2013 to 2021
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Classification:	Mathematics > Differential Equations, Potential Theory, Functional Analysis

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KMA (20.05.2004)

The main task of the calculus of variation is to search and investigate minimizers of functionals on spaces of differentiable functions.

Literature -

Last update: T_KMA (23.05.2008)

Drábek, Pavel; Milota, Jaroslav: Methods of nonlinear analysis. Applications to differential equations. Birkhäuser Advanced Texts: Basler Lehrbücher. Birkhäuser Verlag, Basel, 2007

Dacorogna, Bernard: Direct methods in the calculus of variations. Second edition. Applied Mathematical Sciences, 78. Springer, New York, 2008.

Syllabus -

Last update: T_KMA (23.05.2008)

1. Direct methods of the calculus of variations. Compactness, semicontinuity (also the sequential weak versions), coercivity.

2. Necessary and sufficient conditions for existence of minimizers. Euler-Lagrange equations.

3. Relative extrema in infinitedimensional spaces.

4. Critical points of functionals, mountain pass lemma.

5. Functionals on Sobolev spaces, Carathéodory's conditions.

6. Sequential weak compactness in L1.

7. Integrands convex in the last variable.

8. Rank 1 convexity, quasiconvexity, polyconvexity.

9. Relaxed functionals and relaxation theorems.