Subjects

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

Potential Theory 2 - NMMA464

Title:	Teorie potenciálu 2
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2014
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer 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

Guarantor:	prof. RNDr. Jaroslav Lukeš, DrSc.
Class:	M Mgr. MA M Mgr. MA > Volitelné
Classification:	Mathematics > Differential Equations, Potential Theory
Incompatibility :	NDIR055
Interchangeability :	NDIR055
Is interchangeable with:	NDIR055

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KMA (25.04.2013)

The generalized Dirichet problem is investigated: the Perron-Wiener-Brelot solution, resolutive functions, harmonic measure, regular points, the Green function, capacity. Uniqueness of an operator of the generalized Dirichlet problem is studied. Historical development is summarized and various directions of modern potential theory are indicated (harmonic spaces, relation with Brownian motion).

Literature

Last update: T_KMA (02.05.2013)

Armitage, D. H.; Gardiner, S. J.: Classical potential theory.

Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 2001.

Helms, L. L.: Introduction to potential theory. Reprint of the 1969 edition. Pure and Applied Mathematics, Vol. XXII. Robert E. Krieger Publishing Co., Huntington, N.Y., 1975

Syllabus -

Last update: T_KMA (25.04.2013)

A substantial part of the lecture is devoted to the classical and generalized Dirichlet problem: regular sets, the Perron-Wiener-Brelot solution, resolutive functions, harmonic measure and boundary behaviour of the solution. Properties of the Green function on general domains and the notion of capacity are applied to investigation of the character of the set of irregular points. Also a question of uniqueness of an operator of the generalized Dirichlet problem ( the Keldysh theorem ) is studied. The exposition pays attention to historical commentaries as well as to excursions to modern parts of potential theory.