Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-70-14-K-7

Nonlinear Functional Analysis with Applications to PDE (2V, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h

Basedata

SWS 2V
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Additional informations
Livecycle-State [NORM] Active

Notice

This course cannot be used together with the course [MAT-81-13-K-7] because of large content overlaps.

Contents

From the large field of nonlinear functional analysis, methods and techniques are discussed which play a central role in the investigation of nonlinear elliptic and parabolic partial differential equations. In particular, the following contents are discussed:
  • fixed point theorems,
  • integration and differentiation in Banach spaces,
  • the theory of monotone operators and their applications in the study of nonlinear elliptic and parabolic partial differential equations.

Literature

  • H. W. Alt: Lineare Funktionalanalysis,
  • H. Gajewski, K. Gröger, K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen,
  • D. Gilbert, N. S. Trudinger: Elliptic partial differential equations of second order,
  • E. Hille, S. Phillips: Functional analysis and semigroups,
  • M. Ruzicka: Nichtlineare Funktionalanalysis: Eine Einführung,
  • R. E. Showalter: Monotone operators in Banach space and nonlinear partial differential equations,
  • K. Yoshida: Functional analysis,
  • E. Zeidler: Nonlinear functional analysis and its applications I: Fixed-point theorems,
  • E. Zeidler: Nonlinear functional analysis and its applications II/B.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

Knowledge from the module [MAT-81-11-M-7] is desirable, but not necessarily required.

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-70-14-K-7]

Module Name Context
[MAT-70-14-M-7] Nonlinear Functional Analysis with Applications to PDE P: Obligatory 2V, 4.5 LP