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arXiv · 2001.04914

The Biharmonic Alt-Caffarelli Problem in 2D

Marius Müller
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Abstract

We examine a variational free boundary problem of Alt-Caffarelli type for the biharmonic operator with Navier boundary conditions in two dimensions. We show interior C2-regularity of minimizers and that the free boundary consists of finitely many C2-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.

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Marius Müller. 2020-01-14. The Biharmonic Alt-Caffarelli Problem in 2D. https://arxiv.org/abs/2001.04914

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