Institute of Applied Mathematics
Lecture in Summer Term 2020
Partial differential equations and boundary value problems
Content
  • Sobolev spaces
  • Elliptic differential equations
  • Existence and uniqueness of solutions, regularity
  • Dirichlet, Neumann- and Robin boundary value problems
  • Spectral theory of differential operators, Schrödinger operators
Lecture
Exercises
  • Dr. Markus Holzmann
  • The schedule for the lecture can be found in the TUGonline
  • Criteria for successful completion of the exercises:
    • 50% of the votes,
    • two successful presentations at the blackboard of voted problems
    • one half of the final mark is constituted by the votes and the other half by the presentations
    • after two times voting for an exercise class students will get a grade
  • Online-Kreuzerlsystem
  • Exercise sheets: Sheet 1, Sheet 2, Sheet 3, Sheet 4, Sheet 5, Sheet 6
Textbooks
  • W. Arendt and K. Urban, Partielle Differenzialgleichungen, Spektrum Akademischer Verlag, 2010
  • L. C. Evans, Partial differential equations, Graduate Studies in Mathematics Vol. 19, AMS, 1998
  • G. Grubb, Distributions and operators, Graduate Texts in Mathematics Vol. 252, Springer, 2009.
  • D. Haroske and H. Triebel, Distributions, Sobolev Spaces, elliptic equations, EMS Textbooks in Mathematics, 2008
  • W. McLean, Strongly elliptic systems and boundary integral equations, Cambridge University Press, Cambridge, 2000.