This workshop, sponsered by AIM and the NSF, 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

1. Long and short time existence of solutions to initial value problems for time-dependent Bernoulli and capillary-type free boundary problems.
2. Singularity formation and structure in these dynamic problems.
3. Uniqueness and well-posedness for these flows.
4. Relationships with other geometric flows and dynamical free boundary problems.
5. The Lipschitz and non-degeneracy properties of non-minimizing stationary solutions.
6. The rough regularity of the free boundary (e.g. understanding the topological vs measure theoretic boundary) for non-minimizing stationary solutions
7. The construction of potentially pathological non-minimizing stationary solutions.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org