The Biharmonic Alt-Caffarelli Problem in 2D

2020/01/14 by Müller, Marius · 1 citation
#35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.04914

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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