Seminars & Colloquia Calendar
The Alt-Caffarelli functional with volume constraint.
Dennis Kriventsov, Rutgers University
Location: https://rutgers.webex.com/rutgers/j.php?MTID=m3cd0c939b5693503d0bdf1aa9410b8a6
Date & time: Tuesday, 12 May 2020 at 1:40PM - 3:40PM
Abstract: I will discuss an old, classic example from free boundary theory: minimizing the Alt-Caffarelli functional with volume constraint. The paper is based on an obvious idea: finding it difficult to deal with a constraint, we replace it with a penalization. The catch is that the penalized functional is not differentiable with respect to domain variations, while the estimates available for it all seem to depend on the penalization parameter. This example explains how sometimes, on good days, one may still obtain Euler-Lagrange equations for non-differentiable functionals, and sometimes if you penalize correctly, the penalized and constrained problems turn out to have identical minimizers. While the example is free boundary based, I think the insights are applicable to many calculus of variations problems.
