Variational Methods

Course guarantor:

Lecturer:

Tutor:

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Department of Mathematics

Synopsis:

1. Functional extremum, Euler equations.

2. Conditions for functional extremum.

3. Theorem on the minimum of a quadratic functional.

4. Construction of minimizing sequences and their convergence.

5. Choice of basis.

6. Sobolev spaces.

7. Traces. Weak formulation of the boundary conditions.

8. V-ellipticity. Lax-Milgram theorem.

9. Weak solution of boundary-value problems.

Requirements:

Syllabus of lectures:

1. Functional extremum, Euler equations.

2. Conditions for functional extremum.

3. Theorem on the minimum of a quadratic functional.

4. Construction of minimizing sequences and their convergence.

5. Choice of basis.

6. Sobolev spaces.

7. Traces. Weak formulation of the boundary conditions.

8. V-ellipticity. Lax-Milgram theorem.

9. Weak solution of boundary-value problems.

Syllabus of tutorials:

Study Objective:

Study materials:

Povinná literatura

1. S. V. Fomin, R. A. Silverman: Calculus of variations, Courier Dover Publications, Dover, 2000.

2. K. W. Cassel, Variational Methods with Applications in Science and Engineering, Cambridge University Press, 2013.

Doporučená literatura

3. B. S. Mordukhovich: Variational Analysis and Applications, Springer International Publishing, 2018.

4. F. J. Sayas, T. S. Brown and M. E. Hassell, Variational Techniques for Elliptic Partial Differential Equations : Theoretical Tools and Advanced Applications, Taylor and Francis, 2019

5. B. Dacorogna: Introduction to the Calculus of Variations, Imperial College Press, London, 2004.

6. B. Van Brunt: The calculus of variations, Birkhäuser, Basel, 2004.

7. E. Giusti: Direct methods in the calculus of variations, World Scientific, Singapore, 2003.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: