Sobolev Functions
(Lecture course in Winter Term 2020/21)
Instructor: Anton Treinov
Lecture:
 Uploads on Lecture2Go on Monday and Tuesday (first on January 4th)
Exercise classes :
 Friday, 1214, on BBB (first on January 8th)
More informations and links regarding the lecture and exercise classes will be made available on Stine.
Relevance: The course is eligible as a part of the master in Mathematics, Mathematical Physics, Industrial Mathematics, or Economathematics and is recommended to everyone with interests in analysis. Clearly, other interested participants are also very welcome.
Modular structure and ECTS points: The lecture is a 6ECTS module over the second half of the term.
Prerequisites: The lecture builds on basic knowledge in analysis (including the theory of Lebesgue integration) and some familiarity with functional analysis is recommended. Brief reminders on functional analysis may be given rarely.
Contents:
Sobolev Functions (key topics: weak derivatives, sobolev spaces, sobolev embedding, poincarĂ© inequality, traces).
Literature: Some common books (of different scope) are:
 R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Elsevier, 2003,
 D.R. Adams, L.I. Hedberg, Function Spaces and Potential Theory, Springer, 1996,
 H.W. Alt, Lineare Funktionalanalysis, Springer, 2012,
 L.C. Evans, Partial Differential Equations, American Mathematical Society, 1998,
 L.C. Evans, R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 2015,
 D. Gilbarg, N.E. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 2001,
 E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, 2003,
 G. Leoni, A First Course in Sobolev Spaces, American Mathematical Society, 2009,
 W.P. Ziemer, Weakly Differentiable Functions, Springer, 1989.
