Elliptic Partial Differential Equations (Instead of PDE II)

Elliptic Partial Differential Equations (Instead of PDE II)

Semester
WiSe 2023 / 24

Lecturer
Richard Höfer

Type of course (Veranstaltungsart)
Vorlesung

German title
Elliptische Partielle Differentialgleichungen (anstelle von PDG II)

Contents
In dieser Vorlesung wird das Studium elliptischer partieller Differentialgleichungen zweiter Ordnung aus der Vorlesung "Partielle Differentialgleichungen I" vertieft. Die Inhalte sind disjunkt von den Inhalten der Vorlesung "Partielle Differentialgleichungen II" der vergangenen Jahre. Folgende Inhalte sind geplant:
- Schauder und L^p-Regularitätstheory für lineare Gleichungen über Campanato Räume.
- Harnack Ungleichung und DeGiorgi-Nash-Moser Theorem
- Meyers Abschätzung
- Lösungsmethoden und Regularität für nichtlineare Gleischungen z.B. durch Kompaktheit und variationelle Methoden

English: We continue the study of elliptic partial differential equations from the lecture series "Partial Differential Equation I". The content is disjoint from the content of the lecture series "Partial Differential Equation I" of previous years. The following content is planned:
- Schauder and L^p estimates for linear equations by the Campanato approach
- Harnack inequality and DeGiorgi-Nash-Moser Theorem
- Meyers' estimate
- Existence and regularity for some nonlinear elliptic equations e.g. by compactness and variational methods

Literature
Evans, L.C., Partial Differential Equations, American Mathematical Society.

Gilbarg, D., Trudigern, N.S., Elliptic Partial Differential Equations of Second Order, Springer Verlag.

Giaquinta, M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems

Recommended previous knowledge
Es werden Kenntnisse der Inhalte der Vorlesungen Analysis I-III, Lineare Algebra I-II sowie Partielle Differentialgleichungen I vorausgesetzt. Grundkenntnisse in Funktionalanalysis werden benötigt, insbesondere über schwache Konvergenz und reflexive Banachräume.

English: Knowledge of calculus in several variables, Lebesgue integration theory, linear algebra, ordinary differential equations. Moreover, basic knowledge in (linear) functional analysis is needed. (In particular results on weak convergence and reflexive Banach spaces.)

Time/Date
Lecture: Tuesday 10-12 and Wednesday 10-12, Exercise Group: Wednesday 8-10.

Location
Lecture: M104, Exercise Group: M102

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=62576
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for the exercise classes: During the first weak of the lecture time via 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

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: individual, by appointment, re-exam: Date: individual,
by appointment

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

ECTS
9 ECTS