401-3462-00L  Functional Analysis II

SemesterSpring Semester 2018
LecturersA. Carlotto
Periodicityyearly recurring course
Language of instructionEnglish


AbstractFundamentals of the theory of distributions, Sobolev spaces, weak solutions of elliptic boundary value problems (solvability results both via linear methods and via direct variational methods), elliptic regularity theory, Schauder estimates, selected applications coming from physics and differential geometry.
ObjectiveAcquiring the language and methods of the theory of distributions in order to study differential operators and their fundamental solutions; mastering the notion of weak solutions of elliptic problems both for scalar and vector-valued maps, proving existence of weak solutions in various contexts and under various classes of assumptions; learning the basic tools and ideas of elliptic regularity theory and gaining the ability to apply these methods in important instances of contemporary mathematics.
Lecture notesLecture notes "Funktionalanalysis II" by Michael Struwe.
LiteratureUseful references for the course are the following textbooks:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

David Gilbarg, Neil Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, 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-Verlag, Berlin, 2003.
Prerequisites / NoticeFunctional Analysis I plus a solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).