Partial Differential Equations I

Partial Differential Equations I

Semester
SoSe 2023

Lecturer
Richard Höfer

Type of course (Veranstaltungsart)
Vorlesung

German title
Partielle Differentialgleichungen I

Contents
The lecture series gives an introduction to the theory of partial differential equations (PDEs). In the first part we will study classical solution theories for PDEs. In particular we will discuss some fundamental equations and examples and show limitations of classical solution concepts. In the second part of the lecture series an introduction to the modern theory of PDEs is given, which is based on a weaker notion of solutions and functional analytic concepts. In particular we will study elliptic PDEs. The content of the lecture consists of the following parts:

nonlinear PDEs of first order, method of characteristics
fundamental examples for PDEs of second order
maximum principles for elliptic and parabolic PDEs
distributions and Sobolev spaces
linear elliptic PDEs

Literature

M. Renardy und R. C. Rogers, An Introduction to Partial Differential Equations, Springer, 1993
L.C. Evans, Partial Differential Equations, American Mathematical Society, 1998

Recommended previous knowledge
Analysis I-III, Linear Algebra I: useful, but not necessary: Functional Analysis

Time/Date
Mo. 12-14 and Thu. 8-10

Location
Mo. 12-14 in M104, Thu. 8-10 in M103

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=60022
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for the exercise classes: During the first week of the lecture time in the summer
term 2022 via the course homepage (GRIPS).
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of the maximal points in the
exercise sheets, satisfactory presentation of one solution
For module MV (without mark, "unbenotet"): passing a short oral examination
("Fachgespräch", 15 min.) on the content of the lecture series

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: individual, by appointment, re-exam: Date: individual,
by appointment
Combined exam in agreement with the lecturer in combination with, e.g.: Functional Analysis or
Partial Differential Equation II, oral exam: Duration: 45 minutes, Date: individual, by
appointment

Additional comments
The combined exam is an alternative to the oral examination of 30 minutes.

Modules
BV, MV, MAngAn, PHY-B-WE3, PHY-M-VE3, CS-B-Math4, CS-M-P1, CS-M-P2, CS-M-P3

ECTS
9