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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Modern theory of partial differential equations

The course is not on the list Without time-table
Code Completion Credits Range Language
01PDE Z,ZK 4 2P+1C Czech
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

1. Sobolev spaces.

2. Definition, completeness, examples.

3. Continuous and compact embedding theorems.

4. Trace theorem.

5. Weak solution (importance, derivation of the weak formulation).

6. Elliptic PDE of Second Order.

7. Existence and uniqueness of weak solutions (Lax-Milgram theorem).

8. Regularity of weak solutions.

9. Relation to the calculus of variations, Poincaré inequality.

10. Maximum principle for classical and weak solutions.

Requirements:
Syllabus of lectures:

1. Sobolev spaces.

2. Definition, completeness, examples.

3. Continuous and compact embedding theorems.

4. Trace theorem.

5. Weak solution (importance, derivation of the weak formulation).

6. Elliptic PDE of Second Order.

7. Existence and uniqueness of weak solutions (Lax-Milgram theorem).

8. Regularity of weak solutions.

9. Relation to the calculus of variations, Poincaré inequality.

10. Maximum principle for classical and weak solutions.

Syllabus of tutorials:
Study Objective:
Study materials:

Povinná literatura

1. L. C. Evans: Partial Differential Equations, 2nd ed., American Mathematical Society, Rhode Island, 2010.

Doporučená literatura

2. M. H. Protter, H. F. Weinberger: Maximum Principles in Differential Equations, Springer, New York, 1984.

3. D. Gilbarg, N. S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2001.

4. R. A. Adams: Sobolev Spaces, Academic Press, New York, 2003.

5. G. Leoni: A first course in Sobolev spaces, AMS, 2017.

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-05-28
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