Universität Wien
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250547 VO Methods of Funct. Analysis in part. diff. equation (2006W)

Methods of Functional Analysis in partial differential equations

8.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Vorbesprechung am 10. und 11. Oktober 2006, 10.00 - 12.00 Uhr; A 109 (UZA 4)

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 13.10. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 16.10. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 20.10. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 23.10. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 27.10. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 30.10. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 03.11. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 06.11. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 10.11. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 13.11. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 17.11. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 20.11. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 24.11. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 27.11. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 01.12. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 04.12. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Monday 11.12. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 15.12. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 08.01. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 12.01. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 15.01. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 19.01. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 22.01. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II
  • Friday 26.01. 14:00 - 16:00 Seminarraum 2A310 3.OG UZA II
  • Monday 29.01. 15:00 - 17:00 Seminarraum 2A310 3.OG UZA II

Information

Aims, contents and method of the course

i) Distributions: main operations, change of variables, convolution, Fourier transform.

ii) Sobolev spaces, Sobolev embedding theorems.

iii) Fundamental solutions and Green functions of differential operators.

iv) Pseudodifferential operators: continuity in Sobolev spaces, composition, parametrix.

v) Elliptic partial differential operators and boundary value problems: Shapiro-Lopatinskii condition, Fredholm properties, Schauder a priori
estimates.

Assessment and permitted materials

Minimum requirements and assessment criteria

To give an introduction to the applications of the methods of modern functional analysis to partial differential equations.

Examination topics

Operations with distributions, calculation of their Fourier transforms, construction of Fundamental Solutions and Green Functions, ctiteria of continuity of integral and pseudodifferential operators in Hilbert spaces, application of pseudodifferential operators to elliptic boundary value problems for partial differential operators, construction of the parametrix.

Reading list

[1] A. Komech, Linear Partial Differential Equations with Constant Coefficients, p.127-260 in: Yu.V. Egorov, A.I. Komech, M.A. Shubin, Elements of the Modern Theory of Partial Differential Equations, Springer, Berlin, 1999.

[2] A. Komech, Book of Practical PDEs,
http://www.math.tamu.edu/~comech/posobie

[3] I.M. Gel'fand, G.E. Shilov, Verallgemeinerte Funktionen und das Rechnen mit ihnen, 1967 [German]. (Generalized functions. Vol. I: Properties and operations.
New York and London: Academic Press, 1964 [English].)

[4] W. Rudin, Functional analysis. McGraw-Hill, NY, 1991.

[5] L. Schwartz, Mathematische Methoden der Physik I. Mannheim - Wien - Zürich: Bibliographisches Institut,
B.I.- Wissenschaftsverlag, 1974.

[6] M. Shubin, Pseudodifferential operators and spectral theory. Springer, Berlin, 2001.

[7] M. Taylor, Pseudo differential operators. Springer, Berlin, 1974.

Association in the course directory

Last modified: Sa 02.04.2022 00:24