Quick information: In summer term 2020, I will give a graduate lecture on 'Function Spaces & Potential Theory' within the selected topics series. By the recent outbreak of the corona virus, the lectures will

• take place online. As soon as I have more information, the precise platform will be communicated on this website. We will make use of Zoom - the ID and the password are available on request.

• be available online as videos. The lectures themselves will be broadcasted and provided online afterwards; there will be extensive lecture notes and additional slides.

• These rules apply at least until we are allowed to return to the usual setting - in any case, to have a consistent course framework, all lectures will be provided online (even though we might restart as usual at some later point).

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Target audience: The course itself is designed for Master students (and onwards). Bachelor students (3rd year/6th term of study) are also welcome. The necessary prerequisites for the course are as follows:

• Foundational modules: Analysis 1 - 3, Linear Algebra 1,2,

• Advanced modules: Introduction to PDE (or Nonlinear PDE 1 - at least one of the two), Functional Analysis & PDEs.

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Main references: The course will not follow a particular textbook as I also aim to report on some more recent developments as the course evolves. A preliminary background reading list is as follows:

• Adams, D.R., Hedberg, L.I.: Function Spaces and Potential Theory, Grundlehren der mathematischen Wissenschaften 341, Springer Verlag, 1996.

• Heinonen, J.; Kilepläinen, T.; Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations, Dover Publications, 2006.

• Kuusi, T.; Mingione, G.: Guide to nonlinear potential estimates. Bull. Math. Sci. (2014) 4:1–82.