Department of Mathematics

Functional Analysis II

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Check in the VVZ for a current information.

Start of the lecture: Monday, 22.2.2016
Start of the exercise classes: Monday, 22.2.2016

Prof. D.A. Salamon
Coordinator: Charel Antony


Sobolev spaces, Calderon-Zygmund inequality,
elliptic regularity, strongly continuous semigroups,
parabolic pde's.
The lecture course will begin with an introduction to Sobolev spaces
and Sobolev embedding theorems, a proof of the Calderon-Zygmund
inequality, and regularity theorems for second order elliptic operators,
followed by an introduction to the theory of strongly continuous
operator semigroups and some basic results about parabolic regularity.
Applications to geometry will be included if time allows.


Monday 10 - 12 HG G 5
Thursday 13 - 15
HG G 5

Exercise Classes

Begins first semester week.

Name Time Place
Francesco Palmurella Monday 9-10 HG F 26.5
Alexandru Paunoiu
Monday 9-10
HG G 26.3
Francesco Palmurella
Tuesday 9-10 HG F 26.5


Sheets can be dropped off at F28 into the pigeon hole of your teaching assistant. If you spot any typos or mistakes, you can send an e-mail to the coordinator.

N.B. New exercise sheets will be published on Friday every week and new solutions on Tuesday every week.

Lecture History

The lecture will not take place due to public holidays on: Ascension Day 05/05/2016 and on Pentacost 16/05/2016.

Week 1
Laplace's Equation
Week 2
Laplace's Equation
Week 3
Laplace's Equation
Week 4
Sobolev Spaces
Week 5 Sobolev Spaces
Week 6
Easter Break
Week 7
Sobolev Spaces/ Calderon-Zygmund
Week 8
Week 9
Calderon-Zygmund/ Elliptic Equations
Week 10
Elliptic Equations
Week 11
Maximum Principle/ Parabolic Equations
Week 12
Parabolic Equations
Week 13
Parabolic Equations
Week 14
Parabolic Equations


The first chapter on harmonic functions will follow Chapter 4 of

Fritz John - Partial Differential Equations. 4th Edition 1982- Springer Applied Mathematical Sciences - ISBN: 978-1-4684-0061-8

You can find the .pdf of the 3rd version (while being logged in to ETH network) under:

References for the second chapter on Sobolev spaces are:

- Appendix B of the book

Dusa McDuff, Dietmar Salamon - J-holomorphic Curves and Symplectic Topology. 2nd Edition 2012 - (AMS colloquium publication; vol. 52) - ISBN 978-0821887462

You can find the .pdf of an older version under:

-Chapter 7 of

David Gilbarg, Neil Trudinger - Elliptic Partial Differential Equations of Second Order. 3rd Edition 1998 - Springer Classics in Mathematics - ISBN 978-3540411604

You can find the .pdf of the 2001 version (while being logged in to ETH network) under:

References for the third chapter on Calderon-Zygmund are:

Chapters 4,5,6, 7 and some of chapter 8 (time permitted):

For the fourth chapter on Elliptic Regularity and fifth chapter on the Maximum Principles, you can find the handwritten notes of the coordinator here.

For the last and sixth chapter on Parabolic equations (Heat equation on R^n), you can look at the parabolic manuscript above for chapter three and also on the handwritten notes here.


Information to the exam.


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