Teaching

Winter Semester 2025/26: 

V5B5 Advanced Topics in Calculus of Variations: Free boundary problems

 

  • Tue 10.15-11.45: room 2.040
  • Thu 08.30-10.00: room 1.007

 

Link to Vorlesungsverzeichnis

 

Summary: Free boundary problems are partial differential equations that exhibit a priori unknown interfaces, the so-called free boundaries. Such problems arise for instance in physics, biology, or finance, with a classical example being the melting of ice in water. A central mathematical challenge is to understand the structure and regularity of the free boundary, using tools from PDEs, calculus of variations, and geometric measure theory.

This course gives an introduction to the theory of free boundary problems, focusing on two fundamental models: the one-phase Bernoulli problem and the obstacle problem. For these problems we will discuss basic properties of solutions, the classification of blow-ups, and the smoothness of the free boundary near regular points. If time permits, we will also study the thin obstacle problem and its relation to nonlocal PDEs.

 

Literature:

 

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