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401-3462-00L 10 Credits BSC , DR , MSC D-PHYS , D-MATH

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Functional Analysis II

Lecturers & Examiners: Dr. Alessandro Carlotto

VVZ CR n/a

Last Updated: 2026-02-05 15:54:56

Abstract

Sobolev spaces, weak solutions of elliptic boundary value problems, basic results in elliptic regularity theory (including Schauder estimates), maximum principles.

Objective

Acquire fluency with Sobolev spaces and weak derivatives on the one hand, and basic elliptic regularity on the other. Apply these methods for studying elliptic boundary value problems.

Resources

Literature

Michael Struwe. Funktionalanalysis I und II. Lecture notes, ETH Zürich, 2013/14. Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi. Lectures on elliptic partial differential equations. Springer - Edizioni della Normale, Pisa, 2018. David Gilbarg, Neil Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer, Berlin, 2001. Qing Han, Fanghua Lin. Elliptic partial differential equations. Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011. Michael Taylor. Partial differential equations I. Basic theory. Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011. Lars Hörmander. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. Classics in Mathematics. Springer, Berlin, 2003.

General Information

Language: English
Levels: BSC , DR , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: oral 30 minutes

Course Components

Type	Title	Time & Place	Hours
lecture	Functional Analysis II	Mon 10:15-12:00 (HG G 5) Thu 14:15-16:00 (HG G 5) 03.06 Date 14:15-16:00 (HG G 5)	4 h weekly
exercise	Functional Analysis II Groups are selected in myStudies.	Mon 09:15-10:00 (HG E 33.3) Mon 09:15-10:00 (HG F 26.5)	1 h weekly

Offered In

Mathematics Bachelor
- Core Courses
  - Core Courses: Pure Mathematics
Mathematics Master
- Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Core Courses: Pure Mathematics
Physics Master
- Electives
  - Electives: Physics and Mathematics
    - Selection: Mathematics
High-Energy Physics (Joint Master with IP Paris)
- Electives
  - Optional Subjects in Mathematics
Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)
- Graduate School (Official website of the Zurich Graduate School in Mathematics:)