Abstract
AbstractWe examine a variational free boundary problem of Alt–Caffarelli type for the biharmonic operator with Navier boundary conditions in two dimensions. We show interior $$C^2$$
C
2
-regularity of minimizers and that the free boundary consists of finitely many $$C^2$$
C
2
-hypersurfaces. With the aid of these results, we can prove that minimizers are in general not unique. We investigate radial symmetry of minimizers and compute radial solutions explicitly.
Funder
LGFG
Albert-Ludwigs-Universität Freiburg im Breisgau
Publisher
Springer Science and Business Media LLC
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