论文标题
2D中的Biharmonic Alt-Caffarelli问题
The Biharmonic Alt-Caffarelli Problem in 2D
论文作者
论文摘要
我们检查了具有二维的Navier边界条件的Biharmonic运算符的Alt-Caffarelli类型的差异自由边界问题。我们显示了最小化器的内部C2-定型性，并且自由边界由有限的许多C2-Hypersurfaces组成。借助这些结果，我们可以证明最小化的人通常不是唯一的。我们明确研究了最小化器的径向对称性，并明确调查了径向溶液。
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.
