Partial Differential Equations II

Summer Term 2026

Instructors: Thomas Schmidt (lecture), N.N. (exercise class)

Lecture (first on April 9th):

Mon, 14-16, Hörsaal 5 (MIN-Forum)
Thu, 8-10, Hörsaal 7 (MIN-Forum)

Exercise class (first on April 16th):

Thu, 12-14, Seminarraum 4.2 (MIN-Forum)

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.

ECTS points: The module (consisting of the lecture and the exercise class) has a worth of 12 ECTS points.

Prerequisites: The lecture builds on basic knowledge in analysis (including the theory of Lebesgue integration) and linear algebra. Having attended the preceding PDE lecture or alternatively some general experience with PDE analysis is recommended.

Literature: Common books (of different scope) are:

R. A. Adams, J. J. F. Fournier, Sobolev Spaces, Elsevier, 2003
D. R. Adams, L. I. Hedberg, Functions Spaces and Potential Theory, Springer, 1996
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
J. Jost, Partial Differential Equations, Springer, 2013
G. Leoni, A First Course in Sobolev Spaces, American Mathematical Society, 2009
V. Maz'ya, Sobolev Spaces, Springer, 2011
J. Rauch, Partial Differential Equations, Springer, 1991
F. Sauvigny, Partial Differential Equations (2 volumes), Springer, 2012
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970
M. E. Taylor, Partial Differential Equations (3 volumes), Springer, 1996
W. P. Ziemer, Weakly Differentiable Functions, Springer, 1989