This workshop will be devoted to challenges in the theory of Bernoulli free boundary problems, especially those related to time-dependent dynamics. The workshop will bring together researchers with both dynamical and stationary perspectives on the topic. The goal is to identify challenging open problems and promising directions in order to spur the development of the theory of dynamical Bernoulli problems.
The main focus areas of the workshop are
Dissipative motions related to Bernoulli and capillary-type free boundary problems
Regularity and structure of non-minimizing stationary solutions
Some specific topics of interest include
Long and short time existence of solutions to initial value problems for time-dependent Bernoulli and capillary-type free boundary problems.
Singularity formation and structure in these dynamic problems.
Uniqueness and well-posedness for these flows.
Relationships with other geometric flows and dynamical free boundary problems.
The Lipschitz and non-degeneracy properties of non-minimizing stationary solutions.
The rough regularity of the free boundary (e.g. understanding the topological vs measure theoretic boundary) for non-minimizing stationary solutions
The construction of potentially pathological non-minimizing stationary solutions.
