The Biharmonic Alt-Caffarelli Problem in 2D
Analysis of PDEs
2020-01-15 v1
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.
Cite
@article{arxiv.2001.04914,
title = {The Biharmonic Alt-Caffarelli Problem in 2D},
author = {Marius Müller},
journal= {arXiv preprint arXiv:2001.04914},
year = {2020}
}
Comments
43 pages, 1 figure